The US debt crisis has escalated after Republicans were forced to rewrite their proposal to lift the debt ceiling, because they miscalculated how much the original plan would cut spending.

In an embarrassing development for John Boehner, the Republican Congress speaker, the Congressional Budget Office (CBO) ruled on Tuesday night that his bill would have only cut spending by $850bn (£517bn)over the next decade, not the $1.2tn he had aimed for. Republicans are now racing to rewrite the legislation, and have pushed back a congressional vote on the plan from Wednesday to Thursday at the earliest.

Although Boehner was already struggling to find support for his package, the delay increases the risk that Washington will fail to agree a deal to raise the debt ceiling before 2 August, when the federal government is expected to run out of money.

The dollar dropped against other currencies on Wednesday morning as investors faced the possibility that America could default. Several economists believe the country will lose its AAA credit rating within months, which would push up its borrowing costs, even if the $14.3tn debt ceiling is increased in time.

Stock markets also fell heavily, with the FTSE 100 index down by 76 points, or 1.3%, in afternoon trading at 5852. The Dow Jones index fell 128 points in early trading on Wall Street, to 12373.

The White House said on Tuesday it was working with Congress to devise a "Plan B" that might attract enough support. The two sides have been deeply divided for weeks, with Republicans demanding deep spending cuts and Democrats anxious to include tax rises as a major part of the deal.

The US people may be losing patience with their political leaders. The congressional telephone system was swamped with calls from the public on Tuesday, coming close to collapse. The websites of several members of Congress have crashed this week, after president Obama urged Americans to make their voices heard.

Across the globe, there is growing astonishment that the world's biggest economy is on the brink of a technical default because its elected leaders cannot hammer out a deal. Nouriel Roubini, the leading economics professor, said there was disbelief in China. "Biggest concern in meetings in Hong Kong: will the US default on its debt? Folks here are shocked by the dysfunctional US political system," he tweeted from Shanghai.

Traders are braced for the debt ceiling negotiations to go right to the wire.

"Equity markets remain on the back foot as the US debt impasse continues to dominate the agenda. The political spat continues and as a result the expectation is that negotiations will be ongoing into next week, right up to that August 2nd deadline," said Chris Weston, Institutional trader at IG Markets.

Complacency rules, ok?

Analysts have suggested that America may have more time to resolve the crisis than the government has admitted, with Barclays Capital calculating that the country might be able to function until 10 August before needing to borrow again.

The yield, or interest rates, on US 10-year bonds remained below 3% on Wednesday – meaning America still enjoys some of the cheapest borrowing costs of any country. There are indications, though, that investors are becoming more anxious, with the Chicago Board Options Exchange (CBOE) volatility index, which tracks Wall Street confidence, rising by 4.5%.

"We are finally seeing a little bit of risk priced in, but not a lot is being priced in yet," said Louise Cooper, markets analyst at BGC Partners. "There's still complacency ... I don't think anyone expects this to go wrong."

One possibility is that Obama could approve a short-term rise in the debt ceiling while Congress wrestles with a long-term fiscal plan.

"The can would then be being kicked down the road in the States as well as in Europe," said Cooper, referring to the eurozone's own debt problems.

The Financial Times reported on Wednesday that banks are now holding on to more cash, bolstering their liquidity levels in preparation for a US credit rating downgrade that could potentially prompt a second credit crunch.

"We've been here before, post-Lehman Brothers, and we don't want to be there again," commented Cooper.

The wrangling over the debt ceiling could do long-term damage to America's economic credibility, warned Christopher Molumphy, chief investment officer of Franklin Templeton Fixed Income Group.

"The lack of a credible long-term solution would likely raise questions about the creditworthiness of the US, push up the cost of capital for private and public borrowers and thus prove a further impediment to economic recovery. There is still time for a deal to be reached on raising the debt ceiling, but continued doubts about a longer-term solution to the US's federal deficit may well threaten the country's AAA credit rating and the status of US Treasuries as assets previously perceived as virtually 'risk-free', and against which many other products are gauged," said Molumphy.