Puzder's nomination has emerged of particular interest to Mitch McConnell, the Senate majority leader, who has a long-standing relationship with the nominee. In private meetings with GOP senators, McConnell has told his colleagues that he thinks Puzder is more prepared than any nominee in history to be labor secretary, several sources say. This has surprised some of McConnell's colleagues because his wife, Elaine Chao, served as George W. Bush's labor secretary for eight years, but it underscores the seriousness that the shrewd GOP leader is taking the nomination.
While GOP leaders have expressed confidence that Puzder will be confirmed, some top Republicans privately believe that the battle over the Labor Department nominee could be the most intense of any of President Donald Trump's picks so far.
That's partly because GOP senators have already taken a beating over confirming Betsy DeVos as education secretary, and many are wary about expending even more political capital for another nominee who is bound to prompt an emotional fight -- especially one with significant liabilities before his hearings have even begun.
The most significant: His revelation that he hired a housekeeper from Guatemala who was an undocumented immigrant, only to pay back taxes later.
"I have not reached a decision," said Sen. Susan Collins of Maine. "I almost always wait until there is a hearing unless I know the individual well. I have had two conversations with Mr. Puzder, and I think there are questions outstanding that I'm sure will be ... delved into at his hearing."
And Puzder is at serious risk of losing some swing Democratic votes, meaning Trump cannot afford to lose more than two GOP votes in the Senate to get him confirmed.
"He hasn't gotten through that yet," Sen. Joe Manchin, D-West Virginia, said of Puzder's hiring of an undocumented immigrant. "He's going to have to explain that. That's serious."
At a private meeting in McConnell's office Wednesday night, the GOP members of the Health, Education, Labor and Pensions Committee discussed Puzder's problems, with several raising concerns about the undocumented immigrant, according to several sources.
But McConnell, sources said, made the case that Puzder should not lose sight of the bigger picture: That Puzder has spent many years delving deeply into labor and business issues and that combined with his record running the parent company of the Hardee's and Carl's Jr. restaurant chains, it makes him imminently qualified for the job. McConnell made the case that Puzder acknowledged his "mistake."
Leaving the meeting, some believed the GOP leader would be heavily involved in convincing his skeptical members of to go along with the nomination.
McConnell, in particular, trusts Puzder because of his extensive writings over the years about key policy issues affecting businesses, sources said. And the two have a relationship through the fundraising circuit that McConnell regularly hits.
"He was very effective," said one GOP Senate source who attended the meeting, talking about McConnell's sales job.
Still, several key Republicans on the committee are withholding their support so far, including Collins, Tim Scott of South Carolina, Johnny Isakson of Georgia and Lisa Murkowksi of Alaska.
"It's something that's got to be considered in the totality of the other issues," Isakson said. "When he knew, how we knew, how he found out, what he did afterward ... I'm not prepared to make a definitive statement until I've seen all the facts."
Battling back against liberal groups
What makes things tougher: Puzder's confirmation hearing will take place next week -- right before a week-long Senate recess. That means the confirmation vote will not take place for potentially a few weeks after the hearings, giving opponents time to mobilize against him.
And already, Democrats are ratcheting up their attacks, with Senate Minority Leader Chuck Schumer warning Trump on Thursday that his party is prepared to do battle.
"This is Donald Trump believing he can get away with almost anything," Schumer said Thursday. "He will not be able to."
To counter the battle from the left, McConnell and Sen. Lamar Alexander are hatching their plans. They plan to lean on roughly a dozen outside groups on the right -- including groups that represent home builders, retailers, small businesses and restaurant associations -- to launch a major public relations offensive in support of Puzder.
And they are getting assurances from the White House that it will be more engaged in the effort to confirm Puzder, with hopes that the President will persuade some in the labor community to sit out of the battle.
The cover from the outside was lacking in the DeVos fight -- making things much harder for the GOP as it took a beating from the left. A number of Republicans privately griped about the White House's lack of public push for DeVos as the GOP senators took a brunt of the blame.
Alexander expressed confidence in Puzder's chances.
"I think he's a very talented individual," said Alexander, who chairs the HELP Committee.
But above all else, Republicans need Puzder to have a strong performance at his hearings next week -- to win over GOP skeptics more than anything else.
Beyond Puzder's undocumented immigrant problems, the nominee has other personal issues as well. His messy divorce from three decades ago has entered the media spotlight, when he was accused of domestic abuse at that time, something his ex-wife discussed in disguise on the "Oprah Winfrey Show." But she later dropped the charges, and has since sent a letter to the HELP Committee members vouching for his character and saying she regretted pressing charges.
"Andy is not and was not abusive or violent," said Lisa Fierstein in the January 18 letter to the committee. "He is a good, loving, kind man and a deeply committed loving father."
Yet, Puzder risks putting off senators from the left and the right. Other ideological issues are bound to come up that could spark controversy from liberal groups and some conservatives may be put off by his more moderate immigration positions.
But the Trump administration is expressing confidence.
"The Democrats and their special interests -- and particularly the unions -- have taken their smear tactics to a new level of ugly," said Puzder spokesman George Thompson. "The fact is, Mr. Puzder is exactly what America's workers and businesses need -- a proven job creator."