President Donald Trump’s nominee to lead the Labor Department, Andy Puzder, on Monday admitted to employing an undocumented immigrant, a revelation that has potential to sink his nomination.

“My wife and I employed a housekeeper for a few years, during which I was unaware that she was not legally permitted to work in the U.S. When I learned of her status, we immediately ended her employment and offered her assistance in getting legal status. We have fully paid back taxes to the IRS and the State of California and submitted all required paperwork,” Puzder, the CEO of CKE Restaurants, said in a statement obtained by the Huffington Post.

Puzder’s confirmation hearing has already been delayed by the Senate Committee on Health, Education, Labor and Pensions several times. Most recently, the committee had scheduled a hearing for Feb. 7, but the hearing was postponed indefinitely while the committee waits for Puzder’s documents from the Office of Government Ethics.

It’s also been reported that Puzder’s ex-wife accused him of domestic violence, but Puzder has denied physically abusing her.

Despite the setbacks, it appears that the Trump administration will continue to push Puzder’s nomination. A spokesman for Puzder told the New York Times that he is still “all in” to become the labor secretary.

Sen. Lamar Alexander (R-TN), chair of the HELP Committee, also seemed unfazed by the revelation about Puzder’s undocumented employee.

“Based upon what I’ve learned, since Mr. Puzder reported his mistake and voluntarily corrected it, I do not believe that this should disqualify him from being a Cabinet secretary,” Alexander said in a statement to CNN.

Past nominees, including Bill Clinton’s attorney general nominee Zoe Baird, and George W. Bush’s labor nominee Linda Chavez, both saw their confirmation chances disappear when it was reported that they employed undocumented immigrants.

Trump’s commerce secretary nominee, Wilbur Ross, told the Senate Commerce, Science and Transportation Committee ahead of his confirmation hearing that he fired an undocumented immigrant when he learned of the employee’s legal status.