Van Hollen worked with seven other Democrats to build the case he could defeat Steny Hoyer.
The Senate majority leader faced criticism for his treatment of amendments to the bill.
The Democrat called for reauthorizing the bank in the fast-track trade legislation.
The measure extends federal transportation funding until July 31.
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."