GOP senators have questioned Lew's private-sector experience with both Citigroup and New York University, and the former White House chief of staff's role in previous fiscal negotiations.
But Lew's nomination has not sparked the kind of criticism that another of President Obama's high-profile nominees, Chuck Hagel, has received. The Senate is expected to hold a procedural vote Tuesday on Hagel's nomination for Defense secretary.
Democrats have said that Lew has been exceedingly transparent during his nomination process, and believe he should be confirmed without issue.
Obama nominated Lew to replace Timothy Geithner, who left the Treasury Department in January.
Sen. Orrin Hatch (Utah), the ranking Republican on the Finance panel, declined to say Monday how he would vote on Lew's nomination.
But Hatch did say that, if Lew cleared the committee fairly easily on Tuesday, he didn't see any reason to slow walk the nomination.
"If he comes out of committee, I don't see any reason why anybody would want to continue to put it off," Hatch said. "I can't speak for all my colleagues. All I can say is, we'll see what happens in committee tomorrow."
Sen. Jeff Sessions (R-Ala.), perhaps the chamber's most vocal critic of Lew, continued to blast the nomination on Monday, saying Lew did not have the "gravitas" to be a good Treasury secretary.
But Sessions would not say whether he would push to delay a full Senate vote on the nomination.
This post was updated at 6:45 p.m.