WASHINGTON (AP) — Labor Secretary nominee Andrew Puzder acknowledged Tuesday that he had employed a housekeeper who was in the U.S. illegally, putting him again at odds with President Donald Trump's push to keep jobs in American hands.

Puzder said in a statement that he and his wife were unaware the housekeeper was not legally permitted to work in the U.S. during the years they employed her.

"When I learned of her status, we immediately ended her employment and offered her assistance in getting legal status," Puzder said. "We have fully paid back taxes to the IRS and the State of California."

Puzder spokesman George Thompson said Tuesday that the fast food CEO remains committed to becoming secretary of labor and is working on divesting from his financial holdings.

The revelation about the housekeeper has the potential of complicating a confirmation that already has not gone smoothly. Puzder has acknowledged outsourcing CKE Restaurants, Inc.' s technology help desk, the type of practice Trump also derides as being anti-American worker. His confirmation hearing has been delayed at least three times and has not been rescheduled.

But the chairman of the panel holding that hearing says the housekeeper matter is not a hurdle in itself.

"Since Mr. Puzder reported his mistake and voluntarily corrected it, I do not believe that this should disqualify him from being a cabinet secretary," said Sen. Lamar Alexander of Tennessee, who leads the Senate Health, Education, Labor and Pensions Committee.

Democrats and their allies have piled on with unflattering stories from workers at Puzder's restaurants, and they question how well he can advocate for American workers given that he opposes a big hike in the minimum wage and other labor priorities.

"What we have heard is story after story about how he spent his career squeezing workers for profit, leaving many with lost wages, no financial security, and no retirement," said Democratic Sen. Patty Murray of Washington, the ranking Democrat on the Senate committee that will handle Puzder's confirmation hearing. "If Mr. Puzder ever does come before our committee, he's going to have a lot of explaining to do."

Puzder is the second Trump pick whose nomination has faced questions over their hiring of household workers.

Mick Mulvaney, Trump's pick to run the Cabinet-level White House budget office, had acknowledged that he failed to pay more than $15,000 in payroll taxes for a household worker more than a decade ago. He's repaid the government, and those developments do not seem to be impeding his prospects for confirmation.

Trump has blasted, threatened and tried to charm American companies that have moved jobs overseas or consider it, saying he's sticking up for American workers who aren't feeling the economic recovery and form his political base.

The Huffington Post first reported Puzder's disclosure about the housekeeper.