Rep. Pete GallegoPete Pena GallegoTexas Democrats smell blood in the water for 2018 ObamaCare repeal vote: 15 GOP lawmakers to watch Vulnerable Texas GOP lawmaker survives rematch MORE (D-Texas) on Saturday proposed legislation that would make members of Congress "non-essential" federal workers, which means their pay would be stopped in the event of a government shutdown.

"Congress should work around-the-clock, and do so without pay, to keep the government running," Gallego said Saturday.

His Shutdown Member of Congress Pay Act, H.R. 3215, would amend a 1946 law to deem members of Congress as non-essential workers during a government shutdown. It was introduced just a few days before the government would have to tell non-essential workers to stay at home without pay if the House and Senate can't agree on a funding bill.

But while Gallego's bill might have some appeal this week, it would not immediately effect the current Congress until 2015, even if the House were to pass it. The 27th Amendment to the Constitution says no law varying the compensation of members can take effect until after an intervening election.

Several House members have proposed a new amendment to the Constitution to get around this delay and immediately cut their own pay if they fail to, for example, pass a budget.

Like other Democrats, Gallego criticized House Republicans for passing another short-term spending bill on Saturday that undermines ObamaCare, instead of simply passing a "clean" spending bill.

"Putting the full faith and credit of the United States at risk should never be a debating point," he said. "A shutdown should not even be on the table – this is not rocket science."

But House Republicans say the pressure is on Senate Democrats to find some compromise before government funding expires at the end of Monday.