The freeze on salaries for members of Congress has been in place since 2010.
Sen. Mike Lee sought unanimous consent to take up the House-passed USA Freedom Act.
The bill stalled Attorney General Loretta Lynch's confirmation vote last month.
The Arizona Republican is pressing to end what he suggested was a duplicative program.
Steny Hoyer said the freeze made sense in the past, but may limit those who run for office.
The minority leader said passage would "restore the confidence of the American people."
Senators are under a tight schedule to pass legislation ahead of the Memorial Day recess.
Reps. Blum, Graham and Gosar pushed for a vote on the ban.
Sen. Whitehouse's speech marked the 100th in his weekly climate change series.
Monday's votes were the first of approximately 90 amendments that have been tied to the "fast track" trade legislation.