Meanwhile, a centrist Democratic group is warning that if Congress fails to raise the debt ceiling by Aug. 2 and the country defaults on its debt obligations, the result would be “havoc.”

On Thursday, members of the Congressional Progressive Caucus wrote a letter to President Obama calling for House progressive leaders to be included in the ongoing Blair House negotiations and for the CPC’s 2012 budget blueprint, “The People’s Budget,” to be considered in the talks.

“We believe that outlining clear policy objectives is the only way to frame a serious debate about these issues,” the members wrote. “‘Triggers,’ ‘caps,’ and other process-related budgetary gimmicks serve only to distract attention from the concrete policy ideas needed to solve the problems we face.”

Earlier this week, the Republican Study Committee, a group that comprises more than three-quarters of the House Republican conference, unveiled its outline of House conservatives’ conditions in the upcoming debt-limit fight.

In a letter to House Speaker John Boehner (R-Ohio) and House Majority Leader Eric Cantor (R-Va.), the RSC’s members state that their support for any raising of the debt ceiling will hinge on three factors: the country’s deficit must be cut in half next year; federal spending must be capped at 18 percent of GDP; and Congress must send to the states for ratification a balanced budget amendment including provisions against tax increases and a spending limitation amendment.

The group also states its opposition to a “clean” debt-limit vote, which some House Democrats have called for.

“We must state unequivocally that we will not vote for a ‘clean’ debt ceiling increase,” the RSC members wrote in their letter to Boehner and Cantor. “We share your belief, as articulated in your speech in New York on May 9th, Mr. Speaker, that if we do not reverse the out-of-control spending that has led us here, it would be grossly irresponsible for us to extend the limit on the national credit card.”

Details of the RSC’s plan were first reported by The Hill on Wednesday.

Meanwhile, the centrist Democratic think tank Third Way will circulate to members of Congress next Monday a memo outlining what it says would be “the havoc that default would wreak on retirement accounts, mortgages, access to credit, the stock market, and the dollar.”

The group projects that if the country defaults on its debt, the consequences could include the loss of as many as 642,500 jobs, a one-percent reduction in GDP and a 0.5 percent increase in mortgage rates.

The latest developments in the debt-limit fight come as House members are preparing to return to their districts for a week-long recess, during which lawmakers are likely to hear an earful from their constituents over the federal spending fight.