The government's plan, proposed by Henry Paulson, the US treasury secretary, has been under discussion in congress where legislators have called for changes.
Bush, who backed the plan, appears to be open to Democratic demands to broaden the package to hard-pressed mortgage holders.
A compromise that would give legislators oversight of the deal's implementation, and US taxpayers an equity stake in a bailed-out company, as well as cap the pay of executives of rescued firms had seemed in the works until the White House meeting.
Inside the White House session, John Boehner, the House Republican leader, announced his concerns about the emerging plan and asked that the Republican alternative be considered, aides said.
Senior Democrats put the blame squarely on McCain, saying his decision to endorse the new Republican plan that differs markedly from the one that had been under deliberation for about a week, threw the process into disarray.
"John McCain did nothing to help, he only hurt the process," Harry Reid, the senate majority leader, said after the White House talks.
At an impromptu news conference, Barney Frank, the Democratic chairman of the House of Representatives financial services committee, brandished a single sheet of paper that he said was the sum of new Republican proposals introduced at the last minute after a week of sleepless nights in congress.
But McCain stood by the Republican proposal.
"The plan that has been put forth by the administration does not enjoy the confidence of the American people as it will not protect the taxpayers and will sacrifice Main Street in favour of Wall Street," McCain's campaign said in a statement.
Reflecting the unease of many Republicans at the government's unprecedented intrusion into private enterprise, the new plan calls for an independent entity to dispose of bad assets, and a cut in capital gains tax.
Few Americans support the government's proposed bail-out.
"It needs to be modified so that it helps the everyday person who is losing their home," Carole Bailey, from California, told Al Jazeera.
James Berard, a voter in New York, said: "They should let the companies and the executives suffer, I myself have lost $150,000 from my retirement accounts."
In New York on Thursday, hundreds of labour unionists protested against the plan near the New York Stock Exchange.
"We want our tax dollars used to provide a hand up for the millions of working people who live on Main Street and not a handout to a privileged band of overpaid executives," union leaders said.
McCain has come under fire for bringing presidential race politics into the debate.
Christopher Dodd, the senate banking committee chairman, called the White House meeting, convened by Bush at McCain's request, a "photo op and political theatre that had nothing to do with us getting to work".
But McCain said legislators were on track for a deal and Steve Schmidt, one of his senior advisers, said it was Reid who had said McCain's help was needed to help corral Republican support for the plan.
McCain also said he was "very hopeful that we'll have enough of an agreement tomorrow [Friday] that I can get to" a televised debate with Obama on Friday night in Mississippi.
On Wednesday, McCain urged Obama to postpone the debate - the first of three that may prove pivotal in the November 4 election - a call the Democratic candidate rejected.
Rob Reynolds, Al Jazeera's senior Washington correspondent, said it did appear as if the injection of presidential politics had had an adverse effect on the delicate process of negotiations to come up with a deal.
Asian stocks and the US dollar fell on Friday as the US bail-out plans stalled.
Banks around the world are seeking to ensure a flow of credit amid the financial turmoil.
The Bank of Japan pumped a total of 1.5 trillion yen ($14bn) into the Tokyo money market, according to data on its website, on Friday.
Meanwhile, new evidence of the sector's distress came late on Thursday as the US government shut down Washington Mutual, allowing JPMorgan Chase to buy the bank's operations for $1.9bn.
In Europe, Dutch-Belgium bank and insurer Fortis announced plans to sell additional assets to improve its solvency, in an attempt to reassure customers and investors.
HSBC, the largest European bank, announced it was cutting 1,100 jobs worldwide, "in the light of the current global business and economic environment".
Five hundred of those jobs were to be cut in Britain.