Because of the “outstanding” support she has provided during Mr. Trump’s visits, Ms. Morales in July was given a certificate from the White House Communications Agency inscribed with her name.

Quite an achievement for an undocumented immigrant housekeeper.

Ms. Morales’s journey from cultivating corn in rural Guatemala to fluffing pillows at an exclusive golf resort took her from the southwest border, where she said she crossed illegally in 1999, to the horse country of New Jersey, where she was hired at the Trump property in 2013 with documents she said were phony.

She said she was not the only worker at the club who was in the country illegally.

Sandra Diaz, 46, a native of Costa Rica who is now a legal resident of the United States, said she, too, was undocumented when she worked at Bedminster between 2010 and 2013. The two women said they worked for years as part of a group of housekeeping, maintenance and landscaping employees at the golf club that included a number of undocumented workers, though they could not say precisely how many. There is no evidence that Mr. Trump or Trump Organization executives knew of their immigration status. But at least two supervisors at the club were aware of it, the women said, and took steps to help workers evade detection and keep their jobs.

“There are many people without papers,” said Ms. Diaz, who said she witnessed several people being hired whom she knew to be undocumented.

Mr. Trump has made border security and the fight to protect jobs for Americans a cornerstone of his presidency, from the border wall he has pledged to build to the workplace raids and payroll audits that his administration has carried out.

During the presidential campaign, when the Trump International Hotel opened for business in Washington, Mr. Trump boasted that he had used an electronic verification system, E-Verify, to ensure that only those legally entitled to work were hired.

“We didn’t have one illegal immigrant on the job,” Mr. Trump said then.

But throughout his campaign and his administration, Ms. Morales, 45, has been reporting for work at Mr. Trump’s golf course in Bedminster, where she is still on the payroll. An employee of the golf course drives her and a group of others to work every day, she says, because it is known that they cannot legally obtain driver’s licenses.

A diminutive woman with only two years of education who came to the United States speaking no English, Ms. Morales has had an unusual window into one of the president’s favorite retreats: She has cleaned the president’s villa while he watched television nearby; she stood on the sidelines when potential cabinet members were brought in for interviews and when the White House chief of staff, John Kelly, arrived to confer with the president.

“I never imagined, as an immigrant from the countryside in Guatemala, that I would see such important people close up,” she said.

But Ms. Morales said she has been hurt by Mr. Trump’s public comments since he became president, including equating Latin American immigrants with violent criminals. It was that, she said, along with abusive comments from a supervisor at work about her intelligence and immigration status, that made her feel that she could no longer keep silent.

“We are tired of the abuse, the insults, the way he talks about us when he knows that we are here helping him make money,” she said. “We sweat it out to attend to his every need and have to put up with his humiliation.”

Ms. Morales and Ms. Diaz approached The New York Times through their New Jersey lawyer, Anibal Romero, who is representing them on immigration matters. Ms. Morales said that she understood she could be fired or deported as a result of coming forward, though she has applied for protection under the asylum laws. She is also exploring a lawsuit claiming workplace abuse and discrimination.

In separate, hourslong interviews in Spanish, Ms. Morales and Ms. Diaz provided detailed accounts of their work at the club and their interactions with management, including Mr. Trump. Both women described the president as demanding but kind, sometimes offering hefty tips.

While they were often unclear on precise dates of when events occurred, they appeared to recollect key events and conversations with precision.

Ms. Morales has had dealings with Mr. Trump that go back years, and her husband has confirmed that she would on occasion come home jubilant because the club owner had paid her a compliment, or bestowed on her a $50 or sometimes a $100 tip.

To ascertain that she was in fact an employee of the club, The Times reviewed Ms. Morales’s pay stubs and W-2 forms, which list the golf course as her employer. She also made available her Individual Taxpayer Identification, a nine-digit number that is issued by the Internal Revenue Service to foreigners to enable them to file taxes without being permanent residents of the United States. Having a number does not confer eligibility to work.

The Times also examined the documents Ms. Morales presented as proof that she was entitled to work — a permanent resident card, or green card, and a Social Security card, both of which she said she purchased from someone in New Jersey who produced counterfeit documents for immigrants.

The Times ran Ms. Morales’s purported Social Security number through several public records databases and none produced a match, which is often an indication that the number is not valid. The number on the back of the green card that Ms. Morales has on file at the golf course does not correspond to the format of numbers used on most legitimate resident cards. For example, it includes initials that do not match those of any immigration service centers that issue the cards.

Ms. Diaz produced similar documents, though since she has gained legal residence she has been issued a genuine Social Security card and green card.

The Trump Organization, which owns the golf course, did not comment specifically on Ms. Morales or Ms. Diaz. “We have tens of thousands of employees across our properties and have very strict hiring practices,” Amanda Miller, the company’s senior vice president for marketing and corporate communications, said in a statement. “If an employee submitted false documentation in an attempt to circumvent the law, they will be terminated immediately.”

The White House declined to comment.

Mr. Trump opened the golf club in 2004 and has spent all or part of about 70 days at Bedminster since taking office.CreditChristopher Gregory for The New York Times
That Ms. Morales appeared able to secure employment with what she said were fake documents is not surprising: An estimated eight million unauthorized immigrants are in the labor force, and it is an open secret that many businesses, especially in the service sector, hire them.

Mr. Trump has a long history of relying on immigrants at his golf and hotel properties. Though he signed a “Buy American, Hire American” executive order in 2017 tightening the conditions for visas for foreign workers, his companies have hired hundreds of foreigners on guest-worker visas.

In hiring workers who are already in the United States, employers are required to examine identity and work authorization documents and record them on an employment eligibility form. But companies are not required in most cases to take additional steps to verify the authenticity of documents. Because falsifying these documents is so easy, E-Verify, which is required in 22 states, goes the extra step of checking them against records kept by the Social Security Administration and the Department of Homeland Security.

The federal list posted online of employers who use the E-Verify system includes Mr. Trump’s golf club in North Carolina, a state that requires it, but the Bedminster club in New Jersey, where it is not required under state law, does not appear on the list.

During his campaign, Mr. Trump called for expanding the program to workplaces around the country. So far, that has not happened.

Mr. Trump opened his trophy club in the affluent horse country of Somerset County, N.J., in 2004. After buying the 504-acre property from a group of investors in 2002, Mr. Trump planted a sweeping colonnade of maple trees at the entrance and built two 18-hole golf courses, their design inspired by the gardens of Versailles. The membership initiation fee is more than $100,000.

The property has an estimated 40 to 80 employees, depending on the season; the bulk of the basic service workers are foreign-born. Immigrants keep the greens watered and manicured. They clean and maintain the cottages and suites that surround the junior Olympic-size heated pool.

The president has spent all or part of about 70 days at Bedminster since taking office. He has a two-story residence on the property; his daughter Ivanka Trump and her husband, Jared Kushner, were married at the club in 2009, and also have a cottage.

The job at Bedminster, at which Ms. Morales earns $13 an hour, is one of several she said she has held since arriving in the United States in 1999, crossing undetected into California after a journey of nearly six weeks by bus and on foot.

After she first arrived in Los Angeles, a contact provided her with a false Social Security number and an identification card that she was told would enable her to secure employment. She then flew to New Jersey, where she joined her husband, who had arrived months earlier.

In early 2013, a friend who worked at the Trump golf club told her that management was looking for housekeepers.

Ms. Morales was keen: The pay would be $10 an hour, higher than the $8.25 that she was earning cleaning guest rooms at a hotel.

According to her account, when she arrived for her interview, the housekeeping supervisor showed her around and asked her to demonstrate how she cleaned. The supervisor asked her to report to work the next morning at 6 a.m. — with her documents.

Ms. Morales said she told her she had no legal working documents. “I told her I don’t have good papers. She told me to bring what I used at the hotel,” Ms. Morales recalled.

By the time Ms. Morales was hired, Ms. Diaz had been working at the club since 2010 and had the job of cleaning Mr. Trump’s residence.

She said she washed and ironed Mr. Trump’s white boxers, golf shirts and khaki trousers, as well as his sheets and towels. Everything belonging to Mr. Trump, his wife, Melania, and their son, Barron, was washed with special detergent in a smaller, separate washing machine, she said.

“He is extremely meticulous about everything. If he arrives suddenly, everyone runs around like crazy” because Mr. Trump inspects everything closely, Ms. Diaz said.

She recalled a nervous moment in 2012, when Mr. Trump approached her and asked her to follow him to the clubhouse, a renovated 1930s Georgian manor, where he proceeded to run his fingers around the edges of frames on the wall and over table surfaces to check for dust.

“You did a really great job,” she said he told her, and handed her a $100 bill.

That same year, she said, Mr. Trump had an outburst over some orange stains on the collar of his white golf shirt, which Ms. Diaz described as stubborn remnants of his makeup, which she had difficulty removing.

When Ms. Morales joined the housekeeping team in 2013, Ms. Diaz was in charge of training her, and began to take her to tend to Mr. Trump’s house. In November of that year, when Ms. Diaz quit, Ms. Morales and the housekeeping supervisor took on the job of cleaning Mr. Trump’s house together.

Ms. Morales said she will never forget the day Mr. Trump pulled up to the pro shop in his cart as she was washing its large, arched windows. Noticing that Ms. Morales, who is shy of five feet tall, could not reach the top, he said, “Excuse me,” grabbed her rag and wiped the upper portion of the glass.

Mr. Trump then asked Ms. Morales her name and where she was from, she recalled. “I said, ‘I am from Guatemala.’ He said, ‘Guatemalans are hard-working people.’” The president then reached into his pocket and handed her a $50 bill.

“I told myself, ‘God bless him.’ I thought, he’s a good person,” Ms. Morales recalled.

Soon after Mr. Trump launched his campaign for the presidency, in June 2015, Ms. Morales recalled, one of the managers summoned her to tell her that she could no longer work inside Mr. Trump’s house.

Around the same time, she said, several workers, who she said were also working illegally, had their work days shaved from five days to three days. “The workers panicked. A lot of people just left,” she said.

Two months after Mr. Trump’s inauguration, in March 2017, Ms. Morales said that she and other workers received a new employee handbook.

Under a section titled “Immigration Compliance,” the handbook stated that employees were required to present documents specified by the federal government. “Those that are found to have falsified information will not be eligible for employment,” the handbook stated.

Ms. Morales said she was given a new employment form to sign. She could not understand the form, she said, but her lawyer, Mr. Romero, said it was likely an updated I-9 employment eligibility document — a form that, like the previous one, referenced her falsified documents.

Sometime last year, she said, one of the managers told her she must get both a new green card and new Social Security card because there were problems with her current ones.

Ms. Morales provided a detailed account of what transpired, but it was not possible to independently confirm what happened. According to her recollection, she told the manager that she did not know how to obtain new forgeries.

“I don’t know where to get them,’ ” she said she told him.

The manager, she said, suggested she speak with a maintenance employee who he said knew where to acquire new documents. When the maintenance employee told her that the new papers would cost $165, Ms. Morales told the manager that she did not have the money. “He said, ‘don’t worry. I will lend you the money,’” she said.

Ms. Morales said the maintenance worker drove her to a house in Plainfield, N.J., where she waited in his car while he met with someone inside. Ms. Morales said that she had no record or recollection of the address.

The next day, she said, the maintenance worker brought her a new Social Security card and a realistic-looking green card to replace the one that had “expired.” She said the manager made copies of them for files kept at the club’s administrative headquarters.

Now that Mr. Trump was president, there was more than the usual excitement whenever he arrived. Ms. Morales was still asked to clean Mr. Trump’s residence on occasion, and had to wear a Secret Service pin whenever the president was on site, she said, most likely identifying her as an employee, though the pins did not mean employees had a security clearance.

As the months went on, she and other employees at the golf club became increasingly disturbed about Mr. Trump’s comments, which they felt demeaned immigrants from Mexico and Central America. The president’s tone seemed to embolden others to make negative comments, Ms. Morales said. The housekeeping supervisor frequently made remarks about the employees’ vulnerable legal status when critiquing their work, she said, sometimes calling them “stupid illegal immigrants” with less intelligence than a dog.

Ms. Morales expects she will have to leave her job as soon as her name and work status are made public. She understands she could be deported. On Thursday, she spent the day with her lawyer, and as news of her disclosures spread, she did not answer a phone call from her supervisor at the golf course. She said she did not expect to return to work.

She said she is certain that her employers — perhaps even Mr. Trump — knew of her unlawful status all along.

“I ask myself, is it possible that this señor thinks we have papers? He knows we don’t speak English,” Ms. Morales said. “Why wouldn’t he figure it out?”

Maggie Haberman and Ben Protess contributed reporting from New York. Kitty Bennett contributed research.