On Thursday, the House and Senate adjourned until next week, which means it's too late for either chamber to consider Conyers's bill. But Conyers said Thursday that the cuts should be canceled nonetheless, because Republicans and Democrats are unable to agree on a way to adjust what both parties say is a bad idea.

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"If Congress can't or won't come together to craft bipartisan agreement, I believe we have a duty to avert these catastrophic cuts by any means necessary," Conyers said. "The Cancel the Sequester Act of 2013 would give the leaders of both parties the time needed to reach some consensus on budget issues without forcing the average American to pay the price for Washington's dysfunction."

The Congressional Budget Office says the sequester could lead to 750,000 job losses around the country, but Conyers predicted it would lead to two million lost jobs.

"Cutting two million jobs nationwide and slowing the growth of our gross domestic product by half a percent will barely make a dent in our debt and will result in widespread misery," he said. "It could even throw us back into recession."

President Obama met with congressional leaders Friday morning on the sequester, but most downplayed the chances that this meeting would lead to any quick or easy solution to avoiding the cuts. Republicans have said they oppose the across-the-board nature of the cuts, but have refused to trade the total number of cuts for any increase in taxes.

Democrats, in contrast, have proposed legislation that would raise billions of dollars in new taxes to help offset the cuts.

Reps. Alan GraysonAlan GraysonCould bipartisanship rise with Trump government? Schumer under pressure to add Sanders to leadership team Rubio wins reelection MORE (D-Fla.), Sheila Jackson LeeSheila Jackson-LeeLiberal Dems: Trump filling Cabinet with 'stooges' The right person for State Department is Rudy Giuliani Overnight Regulation: House passes GOP bill targeting last-minute Obama regs MORE (D-Texas) and Frederica WilsonFrederica WilsonOn Africa, will isolationist Trump fight an internationalist Congress? House panel approves juvenile justice reform bill Democrats applaud move to put Tubman on bill MORE (D-Fla.) co-sponsored Conyers's bill.