Negotiations to raise America’s borrowing limit appeared to be veering off track on Tuesday, as Republicans dug in against White House demands to increase revenues and proposed a complicated procedural manoeuvre to avoid default.

Amid a growing feeling of desperation over the budget impasse, Republican leaders suggested they were increasingly pessimistic about the potential for an agreement, blaming President Barack Obama for the stalemate.

“I have little question that as long as this president is in the Oval Office, a real solution is probably unattainable,” said Mitch McConnell, the top Republican in the Senate.

Mr McConnell outlined a parliamentary mechanism that – in a worst-case scenario – would allow the debt limit to be increased without any Republican votes.

Under the proposal, Congress would formally reject a request by Mr Obama to increase the debt ceiling. The president could then veto their denial, and Congress would be unable to override the veto without a two-thirds majority.

According to a Democratic official close to the talks, Mr Obama did not rule out using the manoeuvre if a deal could not be reached. The official suggested that it was a positive sign of Mr McConnell’s commitment to ensuring the US would not default on its debt.

However, Mr Obama signalled that the proposal was not a good option because it would fail to address the country's fiscal challenges.

The McConnell plan would shift the entire political burden of the debt ceiling vote on to the Democrats, making it an unattractive option for the White House.

Even so, some influential conservatives outside Congress dismissed the proposal., a popular Tea Party blog, labelled it the “Pontius Pilate Pass the Buck Act of 2011” and a “historic capitulation”.

Newt Gingrich, the former Republican House speaker who is running for president, said it was “an irresponsible surrender to big government, big deficits and continued overspending”.

The proposal was made ahead of the latest White House summit between Mr Obama and congressional leaders – the fourth in less than a week – designed to break the deadlock.

According to the Democratic official, the talks on Tuesday were constructive because John Boehner, the Republican House speaker, and Mr Obama talked openly about their ambitious plan – since derailed by Mr Boehner in favour of a smaller deal – to cut $4,000bn from the US deficit. The official said the discussion gave Mr Obama an opening to restart a dialogue with Mr Boehner.

Before the meeting, however, Mr Boehner contributed to the darkening outlook by saying that the debt ceiling increase was Mr Obama’s “problem”.

In the meetings, Republicans maintained their stance that a debt ceiling increase could not be accompanied by new tax revenues. Democrats, in turn, reiterated that they would not support significant cuts in entitlement spending if the deal did not include increases in revenue.

The Democratic official said the meeting began with Tim Geithner, the US Treasury secretary, telling the lawmakers and Mr Obama that America was a triple-A rated nation, but that the markets could turn against the US if investors began to doubt the parties’ ability to reach a deal.

Moody’s Investors Service, the rating agency, has indicated that it could put the US on notice for a possible downgrade in mid-July if it did not believe a deal could be reached. Republican and Democratic negotiators will meet again on Wednesday.

The Democratic official suggested that a deal could coalesce around $1,500bn in deficit reduction and could promise savings of up to $3,000bn if it included an enforcement mechanism that would trigger automatic savings in the future.

Charlie Cook, a veteran political analyst in Washington, said the chance of default had risen, even though it remained unlikely.

“For the folks in the market who are absolutely convinced that the US is not going to default, I don’t know how they can be as positive about that now,” Mr Cook said.

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