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 Mark GraysonFlorida's Darren Soto fends off DemĀ challenge fromĀ Alan Grayson Live results: Arizona and Florida hold primaries The Hill's Morning Report: Frustration mounts as Republicans blow up tax message MORE (D-Fla.), Sheila Jackson LeeSheila Jackson LeePatrick backs reparations in unveiling 'Equity Agenda for Black Americans' The US should work to counter India's actions against the people of Kashmir Sheila Jackson Lee tops colleagues in House floor speaking days over past decade MORE (D-Texas) and Frederica WilsonFrederica Patricia WilsonTeacher's union leader: DeVos is 'a cautionary tale' of presidential impact on public education Democratic lawmaker tears into DeVos: You're 'out to destroy public education' Democrats lash out at DeVos over proposed changes to loan forgiveness plan MORE (D-Fla.) co-sponsored Conyers's bill.