Washington barreled closer to crisis Tuesday as House Speaker John A. Boehner and Senate Majority Leader Harry M. Reid scrambled to build support for rival plans to control the national debt, but both appeared doomed without significant bipartisan modifications.

House Republicans delayed a vote on Boehner’s bill, which had been set for Wednesday, after congressional budget analysts dealt the legislation a potentially devastating setback by saying it would save far less over the next decade than the $1.2 trillion advertised. The Congressional Budget Office projected that the spending cuts would save only about $850 billion over that period.

The news from the CBO alarmed conservatives, who were already balking at what they considered timid spending reductions. It also meant Boehner’s bill would not meet his own demand that the cuts exceed the size of the $900 billion debt-limit increase.

House Republicans were racing Tuesday night to rewrite portions of the measure to bring the numbers into line. The vote could now come Thursday.

As Boehner (R-Ohio) pressed toward a cliffhanger vote in the House, President Obama signaled that he would veto the measure because it would force another battle over the debt limit early next year. Meanwhile, Reid (D-Nev.) pronounced the proposal “dead on arrival” in the Senate, where Democrats were struggling to rally votes for their own plan to raise the debt limit by $2.7 trillion — enough additional borrowing authority to cover the nation’s bills into 2013.

The legislative maneuvering played out against a backdrop of public outrage, as the Capitol switchboard became jammed and visitors swamped congressional Web sites, apparently heeding a call Obama made Monday in a prime-time national address for Americans to contact their representatives in Congress.

At the height of the deluge, the Capitol was receiving 40,000 calls per hour — twice as many as normal. Some people encouraged lawmakers to stand firm, others demanded a resolution to the weeks-long stalemate that threatens to undermine the sputtering U.S. recovery and damage the nation’s global standing. Still others were simply worried that the impasse could prevent their Social Security checks from arriving on time.

Kate Cyrul, a spokeswoman for Sen. Tom Harkin, said the Iowa Democrat’s office had received more than 700 e-mails and letters overnight, the majority of which “expressed frustration with the debt process and said that we should reach a compromise.”

The national debt has already hit the $14.3 trillion legal limit. Unless Congress acts by next Tuesday, Treasury officials say they could begin running short of cash for federal health-care and retirement benefits, military salaries and payments due investors, potentially throwing the U.S. government into default for the first time. Even if a default is avoided, credit-rating companies are threatening to downgrade the nation’s AAA rating, a move that could drive up interest rates for governments at all levels, as well as for ordinary Americans. Some Republicans have challenged the Treasury’s warnings and said the economic fallout would be limited.