Mississippi Sen. Thad Cochran, the chairman of the Senate Appropriations Committee, is concerned about Mulvaney's views about defense spending and is uncertain whether he'd be willing to support him, two sources familiar with the matter tell CNN.
At the same time, Arizona Sen. John McCain has railed against Mulvaney's past support for a smaller military budget, and a source familiar with his thinking says that he continues to have concerns about Mulvaney ahead of this week's confirmation vote.
On Wednesday, McCain told CNN that he is "leaning against" Mulvaney's nomination because of the nominee's "continued opposition to defense spending."
If there are two GOP defections, it could force Vice President Mike Pence to break a tie in the Senate, something Pence had to do already when he broke a 50-50 tie for Trump's choice of Betsy DeVos to lead the Education Department -- the first time a vice president has broken a Senate tie for a Cabinet nominee in history.
But a third GOP defection would prevent Mulvaney from getting the job. Sen. Susan Collins of Maine said she hasn't made a "final decision" on Mulvaney but that the congressman told her he would treat budgets differently as director of the White House Office of Management and Budget than he did as a House member from a conservative South Carolina district.
"So I thought that was a good answer but I haven't made a decision yet," Collins said Tuesday. "But it was a good meeting."
The Senate voted Wednesday to clear a filibuster attempt Wednesday but the outcome of the final confirmation vote on Thursday is uncertain.
Mulvaney, who is a leading member of the conservative House Freedom Caucus, has previously railed against growing defense budgets as part of his push for dramatically reducing domestic spending. That, along with his past support for pulling back from military operations in Afghanistan, have prompted sharp attacks from defense hawks like McCain.
"Don't you know where 9/11 came from?" McCain lashed out at Mulvaney during his confirmation hearings last month. McCain ultimately agreed in committee to let Mulvaney's nomination advance to the full Senate, but he said he still harbored concerns and warned he could vote against him on the floor. A source familiar with the senator's thinking says he still has those concerns and is undecided on how he'll vote.
Cochran has not made a public statement about his views on Mulvaney, but sources say he shares views similar to McCain's. Chris Gallegos, a Cochran spokesman, declined to comment other than to say the senator has not yet announced his position on the nomination.