(Adds background on the progressive movement's concerns with Puzder; changes spelling of media keyword to "USA-TRUMP/PUZDER" to correct "PUDZER" to "PUZDER")
By Sarah N. Lynch
WASHINGTON, Feb 7 (Reuters) - U.S. President Donald Trump's choice to lead the Labor Department admitted to employing an undocumented immigrant as a house cleaner, the kind of revelation that derailed Cabinet nominees in previous administrations.
Andrew Puzder, chief executive officer of CKE Restaurants Inc, is one of several Trump nominees who face strong opposition from Senate Democrats and progressive groups.
In a statement late on Monday, Puzder said he and his wife had employed a housekeeper for a few years without being aware that she was not legally permitted to work in the United States.
"When I learned of her status, we immediately ended her employment and offered her assistance in getting legal status," he said in the statement. He said he paid back taxes for employing the maid to the U.S. Internal Revenue Service and to California.
The statement was first reported by the Huffington Post.
Senator Lamar Alexander, chairman of the Senate Committee on Health, Education, Labor and Pensions, the panel that will vet Puzder's nomination, said in a statement that Puzder had reported his mistake and voluntarily corrected it.
"I do not believe that this should disqualify him from being a cabinet secretary," he added.
The disclosure came as Senate Democrats held an all-night session in a final attempt to block the nomination of Betsy DeVos, the billionaire school-choice champion whom Trump nominated to be education secretary.
Puzder's tentative date for a confirmation hearing has been repeatedly postponed, as the committee awaited completion of an ethics review by the Office of Government Ethics.
As of Tuesday, the committee had still not received any of the necessary paperwork on Puzder's nomination, though the Federal Bureau of Investigation background check had been completed, according to a committee aide.
Senator Patty Murray, the ranking Democrat on the panel, said on Tuesday she was troubled by the delay and by stories from workers for CKE's primarily franchised fast-food restaurants who have come forward in recent weeks to complain about wage theft and other labor conditions.
"If Mr. Puzder ever does come before our committee, he’s going to have a lot of explaining to do," she said.
Puzder's nomination has sparked protests around the country by some CKE fast-food workers and the union-backed "Fight for $15" movement to raise the minimum wage to $15 an hour.
Puzder has criticized an overtime rule championed by the Obama administration and opposes raising the minimum wage to $15 an hour.
Additionally, some of CKE's racy advertisements featuring women in bikinis have caused Democrats to ask questions about how Puzder will address sexual harassment in the workplace.
It is unclear whether the issues with hiring an undocumented worker could impede Puzder's confirmation.
Wilbur Ross, Trump's pick for commerce secretary, admitted last month that he recently fired a household employee who could not provide proof of legal status.
A Senate panel later approved his nomination. He was awaiting confirmation by the full Senate.
However, previous presidential appointees have run into problems over immigrant labor - including two former nominees under Republican President George W. Bush and a previous nominee under Democratic President Bill Clinton.
All three of those nominees withdrew their names for consideration after the news came to light. (Reporting by Sarah N. Lynch; additional reporting by Doina Chiacu; Editing by Lisa Von Ahn and Jonathan Oatis)