Democrats were under pressure on Monday by the left-wing of their party to mount a filibuster, a manoeuvre that maintains debate open indefinitely and does not allow for a vote.
But only 25 senators supported the move, when at least 41 were needed.
Alito's nomination now goes for a full Senate vote on Tuesday, where a simple majority in the chamber is needed for confirmation.
Fifty-seven senators out of the 100 in the upper chamber have already said they will vote for Alito.
The Senate Judiciary Committee, charged with vetting the conservative judge's nomination, last week endorsed Alito on a party-line vote, dividing Bush's Republicans and Democrats 10 to eight.
Democrats fear the addition of Alito to the nine-justice high court will undo years of liberal court rulings.
Democrat John Kerry - who lost to Bush in the 2004 presidential election - rallied to the cause, along with Senators Ted Kennedy, Patrick Leahy and Joseph Biden, a possible 2008 presidential hopeful.
The full Senate vote is the final hurdle in the arduous process of becoming a high court justice, one of the most powerful positions in the US, and comes three months after Bush named him to the post.
Democrats also condemned Alito as a right-wing partisan intent on undoing decades of civil rights gains for women, minorities and the poor.