"Members of Congress should not be rewarded for continuing to rack up red ink," Jenkins said Thursday. "When companies report a loss, they do not give their employees a raise. It should be the same for Congress."

Jenkins supported the No Budget, No Pay Act on Wednesday, a bill she said is needed to put pressure on the Senate to pass a budget. Under that bill, members of the House and Senate would have their pay withheld if their respective chamber fails to pass a budget.

"Opposing a vote to put your pay on the line if you fail to do your job is indefensible," she said Wednesday. "The futures of our children and grandchildren are at stake, and America can no longer afford to punt on our debt crisis."

Two Democrats — Reps. David Loebsack (Iowa) and Ann KirkpatrickAnn KirkpatrickGold Star father attacked by Trump steps up role in Dem primaries House Dems highlight promising new candidates Vulnerable House incumbents build up war chests MORE (Ariz.) — proposed their own bill that would cut member pay by 10 percent, and block automatic pay hikes. Loebsack said his proposal, H.R. 398, is meant to ensure Congress shares in the struggles many are facing in the economy.

"In a time when our economy continues to struggle and we face an unsustainable debt, it is more important than ever to hold members of Congress accountable to the citizens that they represent," Loebsack said. "This bill is a simple way to show that Congress is serious about restoring fiscal discipline to reform the pay system that has prevented any cut in congressional pay since 1933 — eight decades ago."

Also Wednesday, Rep. Tom Latham (R-Iowa) proposed H.R. 397, which is similar to the No Budget, No Pay Act approved that day. Latham's bill would withhold member pay unless a concurrent budget resolution is adopted by May 15.

Some have criticized the No Budget, No Pay Act because it only requires the House and Senate to pass their own budgets, but it does not require them to agree on a final budget plan. Latham's bill is different in that it requires both chambers to agree on a budget, and also makes this change permanent.

"It's not an unreasonable request to ask the Senate to pass a budget, but for as long as that chamber — and as a result, Congress — fails to get the job done, there should be stiff penalties in place," Latham said. "Our mounting debt won't wait for us to act, and we need to get in front of this generation-defining problem now."

These bills are just the latest proposals to cut or freeze congressional pay, many of which were introduced during the first week of the new Congress.