"We will have a vote when we get back, and I am confident that Senator Hagel will probably have the votes necessary to be confirmed as the secretary of defence," Arizona Senator John McCain, who has led the opposition against his former Republican colleague, told NBC's "Meet the Press" program.
Democrats, who control the Senate, have scheduled a vote for February 26, after members return from a week-long recess. Republicans held up the nomination last week in a delay characterised as the first time the Senate had used a procedural tactic called a filibuster to block a defense nominee.
With Democrats holding 55 votes in the 100-seat Senate, Hagel's nomination is expected to win the simple majority of 51 votes needed for his confirmation to become the civilian leader at the Pentagon, once such a vote is allowed.
If confirmed, Hagel, a 66-year old decorated Vietnam War veteran, would replace 74-year-old Leon Panetta.
Hagel, who broke from his party as a senator by opposing former President George W. Bush's handling of the Iraq War, has faced withering criticism from Republicans since Obama nominated him on January 7 to be the defence secretary.
Some Republicans have questioned if Hagel is sufficiently supportive of Israel, tough enough on Iran or capable of leading the Pentagon. McCain continued on Sunday to voice concern.
"I don't believe he is qualified. But I don't believe we should hold up his nomination any further because I think it is a reasonable amount of time to have questions answered."