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“We acknowledge that we have to be sure that there is a backup plan, because the United States will not default,” Mr. Carney said.

Some conservative lawmakers are furious with Mr. McConnell for issuing the proposal last week, contending it would allow Mr. Obama to continue a spending spree without a commitment to significant deficit reduction.

While the Gang of Six plan was gaining momentum in the Senate, some lawmakers pointed out that it is not yet a piece of legislation and that they were reluctant to sign on.
Sen. Jeff Sessions of Alabama, the senior Republican on the Senate Budget Committee, said the bipartisan Senate plan has “serious flaws.”

Mr. Sessions said the plan makes broad and misleading assumptions, particularly when tabulating spending cuts and how much tax revenue the plan would generate.

“After months of their meeting and working, I had sincerely hoped the Gang of Six would come forward with an actual legislative proposal,” he said. “Unfortunately, we have only vague language and talking points that create more questions than answers.”

But Mr. Obama faces heat on his left flank as well. Many liberals said he has agreed to tax cuts that go much too far.

Sen. Bernard Sanders, Vermont independent and one of the most liberal members of Congress, issued a statement Wednesday to mockingly “congratulate” Republicans on the bipartisan panel for “their long-term goal of dismantling every major social program relevant to working families.”

Richard Trumka, head of the AFL-CIO, blasted the emerging compromise.

“We keep seeing bipartisan support for plans like the so-called ‘Gang of Six’ that cut Social Security benefits, kill jobs, give tax incentives for corporations to export good jobs overseas, tax health benefits, and lower tax rates for billionaires and corporations,” Mr. Trumka said in a statement. “There’s no shared sacrifice here. The only sacred cows being gored are working people, the middle class, seniors and the poor.”

• Sean Lengell contributed to this report.