The conventional wisdom in Washington is that the committee will approve Hagel by a party-line 14-12 vote. That would send the nomination to the full Senate.
Some Republicans, such as Sen. Jim Inhofe of Oklahoma, have said they'll attempt to hold up a vote. They'll try to insist that 60 senators must first agree that there should be a vote on the nomination before there can be a vote. In other words, they'll demand a vote on whether to vote.
But The Associated Press notes that Democrats control 55 Senate seats (two are held by independents who caucus with the Democrats) and that:
"Two Republicans — Sens. Thad Cochran of Mississippi and Mike Johanns of Nebraska — have said they will vote for the nominee. At least five Republicans, including [Arizona Sen. John] McCain, have said they oppose a filibuster despite their reservations or opposition toward the nominee."
So, it would seem there's a fair chance the push to delay a vote won't work — at least not for long.