That Amendment says, "No law, varying the compensation for the services of the Senators and Representatives, shall take effect, until an election of representatives shall have intervened."

But many members argued that the Amendment was really meant to ensure that Congress doesn't immediately raise its pay. Barrow's resolution would repeal the 27th Amendment, and create a new amendment that allows Congress to pass laws that immediately cut their pay.

"The 27th Amendment to the Constitution was written to prevent members of COngress from giving themselves pay increases, but lately it's been used as a shield to prevent a congressional pay cut," Barrow said on the House floor.

"My proposal, H.J.Res. 33, would return the 27th Amendment to its original intent, and hold members of Congress to the same standard as folks back home."

Barrow's new amendment would read, "No law increasing the compensation for the services of the Senators and Representatives shall take effect until an election of Representatives shall have intervened."

Earlier this month, Rep. Ron DeSantis (R-Fla.) proposed another way around the problem — by requiring congressional salaries to be cut by 8.2 percent starting in 2015. DeSantis said that would ensure members feel the bite of the sequester, which took place in March but did not affect members of Congress.