Los Angeles, California (CNN) -- Meg Whitman, California's Republican nominee for governor, denied Thursday ever seeing a letter from the federal government questioning her former housekeeper's Social Security number.

Whitman said she would be willing to take a polygraph test, to prove that she was "really stunned" to learn just last year that Nicky Diaz Santillan was an undocumented worker.

Lawyer Gloria Allred, who represents Santillan, on Thursday released a copy of a 2003 letter from the Social Security Administration that she called "the smoking gun or smoking document" to prove Whitman knew her housekeeper was working illegally in the United States.

Whitman, at a news conference an hour earlier, insisted she and her husband never saw such a letter. She said Santillan sorted their mail and "might have been on the lookout for that letter."

The letter, shown to reporters Thursday afternoon, included a handwritten notation that Allred said was written by Whitman's husband, Dr. Griffith Harsh.

"Nicky Please check this Thanks," is scribbled at the bottom of the letter addressed to Whitman and her husband.

Santillan kept the letter after Harsh gave it to her and the information requested by the Social Security Administration was not provided, Allred said.

"Now that we've shown you the evidence, let's see if she's going to deny it,"Allred said.

Whitman, at a news conference a few miles away and an hour earlier, said she would take a polygraph test to prove she did not know her housekeeper was undocumented "If it comes to that."

"I would be delighted to do that," Whitman said.

The allegations became public Wednesday when Allred held a news conference with Santillan to say the former housekeeper was "exploited, disrespected, humiliated and emotionally and financially abused" by the former eBay CEO.

"Make no mistake, these allegations are completely untrue they lack any merit whatsoever," Whitman said Thursday.

Whitman called the charges a "political smear" orchestrated by her Democratic opponent, Jerry Brown.

Allred said Thursday she has had no contact with the Brown campaign.

The Whitman campaign gave reporters copies of immigration and IRS forms it said Santillan signed stating she was a legal resident of the United States when she first applied for employment as a housekeeper in 2000.

Allred claimed that back in August 2000, Santillan "was sent by an employment agency to interview with Meg Whitman for a job as a housekeeper. ... Nicky alleges that Ms. Whitman never asked if [she] was here legally," Allred said.

"The inconvenient truth of the hypocrisy of Meg Whitman as illustrated by her employment of an undocumented worker and her exploitation of her was going to be revealed, because Nicky wanted to be legalized," Allred said.

"Nicky was terminated in a sudden, cruel and heartless way," she added.

Allred said Santillan intends to file a claim for unfairly denied wages.

Whitman said she paid her housekeeper $23 an hour to work 15 hours a week. Sometimes, she said, Santillan worked fewer hours but was paid for more.

While Whitman called Santillan like a member of her family, the housekeeper described a cold Whitman firing her for political reason.

"When I met with Meg Whitman on June 20, 2009, I asked her for assistance," Santillan said. "I explained to her why I came to the United States. I explained that I was married and our economic situation in Mexico was very bad. We had no job, no food, no place to live and for that reason we made the decision to come here."

"Ms. Whitman just laughed," Santillan said. Whitman, Santillan claimed, also blamed herself for failing to previously ask for any documentation.

Whitman, according to Santillan, indicated four days later that she couldn't help the former housekeeper.

"She said, 'I cannot help you and do not say anything to my children. I will tell them you already have a new job and that you want to go to school and from now on, you don't know me and I do not know you. You have never seen me and I have never seen you. Do you understand me?'"

Allred also outlined what she said were abusive labor practices by Whitman, including not reimbursing the maid for mileage when she ran errands and not allowing her maternity leave.

"When Nicky indicated to Ms. Whitman in March 2005, that she needed to take a medical leave of absence for pregnancy, she alleges that she was told that unless she herself obtained someone to replace her, that her job might not be there for her when she returned."

Whitman denied the allegation, saying Santillan proposed the idea of having a friend fill in for her while she gave birth.

While Santillan used her personal car to "run a few errands," she never asked for mileage reimbursement, Whitman said.

Whitman has previously beat back allegations she was involved in a 2007 shoving altercation with an employee at eBay's California headquarters after the Silicon Valley chief felt unprepared for an upcoming media interview. The incident reportedly led to a $200,000 settlement.

Responding to the press conference, Whitman campaign lawyer Tom Hiltchak told reporters that, when hired in 2000, Santillan gave Whitman false documentation, including IRS forms, a Social Security card, a California drivers license, and Department of Justice immigration forms in which the stated she was in the United States lawfully.

Whitman is currently neck and neck with Brown in the polls.

The issue of immigration looms large in California, as in other states along the Mexican border. Whitman has come out against Arizona's controversial new anti-illegal immigration law, as well as California's controversial Proposition 187. However, she supports tough crackdowns on employers who hire illegal immigrants, requiring employers "pay a fine and have their business license suspended for 10 days" for first-time offenses, with steeper fines and penalties for repeat offenders.