Senator Harry Reid of Nevada, the majority leader, scheduled the vote on the student measure, which is known as the Dream Act, late on Thursday. The Senate will vote on a version of the bill that passed the House of Representatives on Dec. 8.
The bill gained some momentum after passing the House by 20 votes, including 8 Republicans, a wider margin than its supporters had expected. But on Friday the Senate count appeared to be short of the 60 votes Democrats need to bring the bill to the floor for debate. Its sponsors, including Senator Reid and Senator Richard J. Durbin of Illinois, the second highest Democratic leader, acknowledged they faced an uphill climb.