In a written statement, Senate Majority Leader Bill Frist said he looks forward to a "fair up-or-down vote" swiftly on Alito, President Bush's choice to succeed retiring Justice Sandra Day O'Connor.
Alito, 55, an appeals court judge, is assured of approval in the committee, where all 10 Republicans have indicated their support.
Prospects for confirmation in the full Senate are strong, as well.
Democrats have not yet ruled out mounting a filibuster to delay or prevent a final vote. But that appears increasingly unlikely in the wake of Alito's testimony at confirmation hearings last week, where he parried sharply worded Democratic attacks on his judicial record and personal credibility without a major stumble.
The hearings concluded last Friday, and Sen. Arlen Specter, R-Pa., the committee chairman, said he intended to schedule a committee vote for this week on the nomination.
Democrats said at the time that they intended to object, and they did.
Under the rules, any senator can force a delay in a vote for one week.
Democrats said they wanted to give senators time to observe a three-day holiday weekend without coming back to face an immediate vote. At the same time, they came under pressure from outside interest groups that want as much time as possible to try to rally public opposition to the nomination.
"This is a key swing vote on the Supreme Court and Democrats are not going to be rushed into anything," said Jim Manley, a spokesman for Senate Democratic leader Harry Reid of Nevada.
O'Connor has cast the decisive fifth vote on cases upholding the right to an abortion, affirming affirmative action and limiting the application of the death penalty.
Her position as the key swing vote heightened the political stakes for Alito's nomination, with conservatives hoping he will swing the court to the right, and liberals fearful of the same thing.
So far, none of the Senate's 55 Republicans has announced opposition to Alito's nomination, meaning he can be confirmed with GOP votes alone, barring an increasingly unlikely Democratic filibuster.