"If the House can vote on something on a simple majority, so can we," Reid said.
House Republicans meanwhile plan to bring up and defeat an earlier version of Reid's bill Saturday in an attempt to force him to compromise. Reid's gambit with the House bill was intended to show Republicans that their plan would not pass muster in the Senate.
Democrats hoped that with the House bill defeated in the Senate, Boehner and McConnell would re-engage with Democrats in talks on a package that can end the partisan stalemate before Aug. 2.
But Boehner spokesman Michael Steel said the burden is on Reid.
"For the second time, the House has passed a reasonable, common-sense plan to raise the debt limit and cut spending and, for the second time, Sen. Reid has tabled it," Steel said. "The responsibility to end this crisis is now entirely in the hands of Sen. Reid and President Obama."
But other GOP aides said it now appears likely that Boehner will end up being forced to accept a deal which both the Senate and the White House can agree to. Doing so will mean losing significant parts of his own Conference, and will require Boehner to work with House Minority Leader Nancy Pelosi (D-Calif.) to cobble together enough Democrats and moderate Republicans to pass it in the House.
As of late Friday night, no bipartisan talks were scheduled to resolve the impasse.
John Stanton and Humberto Sanchez contributed to this report.
Terri Henderson, 6, center, whose mother is El Salvador, attends a rally with members of Congress at Union Station's Columbus Circle to announce the Restore Opportunity, Strengthen, and Improve the Economy (ROSIE) Act on July 29, 2014. The legislation provides incentives for government contractors to pay a living wage and other benefits that would help low-income workers.