The back and forth began when House Republicans rolled out a two-stage deficit reduction plan that would allow the $14.3 trillion federal debt limit to rise immediately by about $1 trillion in exchange for $1.2 trillion in spending cuts, and tie a second increase early next year to the ability of a new bipartisan Congressional committee to produce more deficit reduction measures.

Mr. Reid dismissed the House Republican plan as a “nonstarter” and said Republicans were essentially trying to embarrass Mr. Obama in the middle of the 2012 election year by forcing another debt limit showdown. He said Democrats would not go along with any plan that did not guarantee a debt limit increase through next year.

Democrats countered with a $2.7 trillion menu of spending cuts and an increase in the debt limit through 2012. Neither plan would require any new revenue.

The approach assembled by Mr. Reid quickly received the president’s endorsement. Over the next 10 years, it would cut $1.2 trillion from federal agency budgets and wring savings from recurring programs like agriculture subsidies. Like some earlier Republican plans, the plan also counts about $1 trillion in savings from winding down combat operations in Iraq and Afghanistan, a point objected to by House Republicans who consider such savings as budget trickery since they would occur regardless.

“The plan is full of gimmicks,” Mr. Boehner told reporters about the Reid proposal, saying it makes no “real changes in the spending structure of our government, and it doesn’t deal with the biggest drivers of our deficit and our debt, and that would be entitlement programs.”

Rushing to beat the Senate to the punch, House Republican leaders were hoping to win approval of their measure on Wednesday and then send it to the Senate. The plan would cut current spending and put legal limits on future spending, saving what Republicans estimate to be about $1.2 trillion over 10 years. That approach would allow a debt limit increase that would extend into early next year.

At the same time, a new 12-member committee evenly divided between Democrats and Republicans would be assigned the job of finding an additional $1.8 trillion in savings. The panel would have special privileges to bring legislation before the House and Senate, and its proposal would not be subjected to amendment or Senate filibuster. If the plan passed, the president could seek a further $1.6 trillion increase in the debt limit based on the new committee’s proposal.