Democrats countered quickly with an alternative that drew presidential backing, and Obama readied a prime-time, nationally televised speech on short notice.
Despite warnings to the contrary, U.S. financial markets appeared to take the political maneuvering in stride. Wall Street posted losses but with no indication of panic among investors.
Without signed legislation by day's end on Aug. 2, the Treasury will be unable to pay all its bills, possibly triggering an unprecedented default that officials warn could badly damage a national economy struggling to recover from the worst recession in decades.
On a day of political jousting, Senate Republican leader Mitch McConnell urged Obama to shift his position rather than "veto the country into default."
On the other side, Senate Majority Leader Harry Reid jabbed at tea party-backed Republicans who make up a significant portion of the House GOP rank and file. The Nevada Democrat warned against allowing "these extremists" to dictate the country's course.
Obama wants legislation that will raise the nation's debt limit by at least $2.4 trillion in one vote, enough to avoid a recurrence of the acrimonious current struggle until after the 2013 elections.
By design or not, the two sides' harsh remarks obscured concessions that narrowed the differences among the nation's political leaders as they groped for a way to resolve the economic crisis.
With their revised plan, House Republicans backed off an earlier insistence on $6 trillion in spending cuts to raise the debt limit.
And Obama jettisoned his longstanding call for increased government revenues as part of any deficit reduction plan.
Pending the president's televised speech, the White House also declined repeatedly to say whether Obama would veto the revised House measure.
House Speaker John Boehner's legislation would provide for an immediate $1 trillion increase in the government's $14.3 trillion debt limit in exchange for $1.2 trillion in cuts in federal spending.
It also envisions Congress approving a second round of spending cuts of $1.8 trillion or more in 2012, passage of which would trigger an additional $1.6 trillion in increased borrowing authority.
Video: Sen. Schumer: Hopeful over Harry Reid's plan (on this page)
The two-step approach runs afoul of Obama's insistence that lawmakers solve the current crisis in a way that avoids a politically charged rerun next year in the middle of the election campaign.
Stopping short of a veto threat, White House communications director Dan Pfeiffer called the proposal "not a serious attempt to avert default because it has no chance of passing the Senate."
Among House conservatives who have provided the political muscle for the Republican drive to cut spending, the revised legislation was a disappointment. "I cannot support the plan," said Rep. Jim Jordan of Ohio, one of the leading advocates of legislation that cleared the House last week and died in the Senate.
Video: Both parties prepare fallback debt plans (on this page)
But two rank-and-file Republicans said their constituents were voicing concerns other than the rising federal debt.
Rep. Tom Rooney, R-Fla., said his office is getting calls from constituents saying, "If I don't get my Social Security check, it's your fault."
Rep. Tom Reed, a New York freshman, said many of his constituents are telling him to stand firm in his drive to cut spending. "But I will admit there's some anxiety in the district" about Social Security and other programs, he added.
As Boehner readied his legislation, Senate Democratic leaders called a news conference to announce their own next steps.
The Democrats' measure would cut $2.7 trillion in federal spending and raise the debt limit by $2.4 trillion in one step — enough borrowing authority to meet Obama's bottom-line demand.
The cuts include $1.2 trillion from across a range of hundreds of government programs and $1 trillion in savings assumed to derive from the end of the wars in Afghanistan and Iraq. The legislation also assumes creation of a special joint congressional committee to recommend additional savings with a guaranteed vote by Congress by the end of 2011.
Yet in the maneuvering it appeared another of the president's long-held conditions appeared to be in danger of rejection.
Neither Boehner's measure nor the one Reid was drafting included additional revenue, according to officials in both parties.
In addition to a two-step approach to raising the debt limit, the House measure would require lawmakers in both houses to vote later this year on a constitutional amendment requiring a balanced federal budget.