In a moment of calculated political theatre, Republicans introduced and then voted down their own measure to increase national borrowing above its current ceiling of $14.3 trillion (87.5trn).
In so doing they sent a clear message to the White House that they would not entertain raising the deficit limit without first seeing deep cuts to expenditure, running into trillions of dollars.
Mr Obama met with Republican politicians yesterday over proposals to curb America's record national debt.
House leaders said discussion inside the White House had been "frank" and "productive".
But it is unlikely to avert a tense game of brinkmanship in the weeks ahead as negotiators race against time to strike a deal.America officially hit its debt ceiling in mid-May, since when officials have been juggling finances to service debt.
The Treasury has said it only has the means to continue doing this until 2 August. If the ceiling isn't increased by that date, the government would have to start defaulting on its obligations.
Doing so would result in "Armageddon-like" consequences for the economy, the White House has previously said.
It would also unnerve the markets and could see the US slide back into recession, some economists predict. Republican leaders have repeatedly asserted they will not agree to greater borrowing unless trillions of dollars are first stripped from government spending. Yesterday House Speaker John Boehner released a statement, signed by more than 150 economists, calling for cuts that would exceed any rise in the debt limit.
It said: "Increasing the debt ceiling without significant cuts and budget reforms will send a message to American job creators that we still are not serious about ending Washington's spending addiction."
The move followed a largely symbolic vote in the House of Representatives the night before. Republicans introduced a measure to raise the cap by $2.4trn only to then vote against it. The bill - which failed by a 318-97 margin - was designed to show the White House that any plan that does not commit to drastic cuts is a non-starter.
But the tactic was attacked by Democrats. Representative Sander Levin accused Republicans of a "ploy so egregious that [they] have had to spend the last week pleading with Wall Street not to take it seriously and risk our economic recovery." The vote took place in the evening so as not to unsettle stock markets.
The move was also seen as an attempt by conservatives to seize back political initiative and draw attention from a deeply unpopular plan to overhaul Medicare, the state healthcare provision for pensioners.
Last week Republican senators were railroaded by Democrats in the upper house into going on record supporting proposals to convert Medicare into a cheaper, voucher-based system.
Republicans are pushing for massive cuts to healthcare in any final deal over the debt ceiling.