That could help ease a crisis of confidence in the banking system, said chairman Sheila Bair.
President Bush spoke with both nominees during the day and made another statement in the White House. "Congress must act," he demanded in front of the cameras.
As the pace of legislative jockeying quickened, the atmosphere on Wall Street seemed to be improving. The Dow Jones industrials rose some 485 points on the day after they had plunged 778. But more attention was on credit markets as a key rate that banks charge each other shot higher, further evidence of a tightening of credit availability.
"I recognize this is a difficult vote for members of Congress," Bush said. "But the reality is we are in an urgent situation and the consequences will grow worse each day if we do not act."
Republican House aides said the FDIC proposal might attract some conservatives who want to help small business owners and avert runs on banks by customers fearful of losing their savings.
House Republican leader John Boehner welcomed McCain's and Obama's embrace of a higher insurance cap, saying congressional Democrats had rejected it Saturday.
Another possible change to the bill would modify "mark to market" accounting rules. Such rules require banks and other financial institutions to adjust the value of their assets to reflect current market prices, even if they plan to hold the assets for years.
Some House Republicans say current rules forced banks to report huge paper losses on mortgage-backed securities, which might have been avoided.
Liberal Democrats who opposed the bill are suggesting other changes. Their ideas include extending unemployment insurance and banning some forms of "short selling," in which investors bet that a stock's value will drop.
The White House signaled a willingness to accept some changes to the bill. Spokesman Tony Fratto said there are plenty of good ideas to help the financial markets and "we're going to look at all of those."
Senate Banking Committee Chairman Christopher Dodd, D-Conn., told reporters, "I'm told a number of people who voted 'no' yesterday are having serious second thoughts about it." He added, however, "There's no game plan that's been decided."
Senate Republican Leader Mitch McConnell of Kentucky said it was time for all lawmakers to "act like grown-ups, if you will, and get this done for all of the people." He predicted a bill would pass this week, although the House, not the Senate, is the focus of the dispute.
The House on Monday balked at approving the measure, pilloried in many quarters as a handout to big business. The 228-205 vote sparked the largest sell-off on Wall Street since shortly after the Sept. 11, 2001, terror attacks.
Bush noted that the maximum $700 billion in the proposed bailout was huge, but was dwarfed by the $1 trillion in lost wealth that resulted from Monday's stock market plunge.
"Because the government would be purchasing troubled assets and selling them once the market recovers," he said, "it is likely that many of the assets would go up in value over time. Ultimately, we expect that much - if not all - of the tax dollars we invest will be paid back."
"The dramatic drop in the stock market that we saw yesterday will have a direct impact on retirement accounts, pension funds and personal savings of millions of our citizens," Bush said. "And if our nation continues on this course, the economic damage will be painful and lasting."
Some lawmakers reported a shift in constituent calls pouring into their offices. Calls and e-mails were overwhelmingly opposed to the rescue plan before Monday's vote, many offices said. But Monday's stock market dive prompted calls Tuesday from Americans furious about Congress' inaction, some said.
Rep. John Campbell, R-Calif., who voted for the legislation, said, "The calls now are saying, 'I lost 10 percent of my retirement yesterday,"' Campbell said. "The calls I'm getting are thanking me now."
But Joseph Brettell, a spokesman for Rep. Marilyn Musgrave, R-Colo., said calls to her office remain overwhelmingly supportive of her "no" vote.
House Republicans, meanwhile, stopped blaming Monday's outcome on criticisms of the GOP that Speaker Nancy Pelosi, D-Calif., included in her address to the chamber shortly before the vote. On Monday, House GOP leaders said her partisan remarks caused a dozen Republicans to vote against the bill instead of for it.
Democrats rebuked Republicans for basing a crucial vote on pique instead of conviction, and Republicans dropped the claim Tuesday. Rep. John Shadegg, R-Ariz., told MSNBC he did not base his "no" vote on Pelosi's remarks, adding, "I don't know a single Republican who did."
On Tuesday, Pelosi and Reid wrote to Bush, saying, "We welcome your statement this morning and are committed to working with you and our Republican colleagues to enact a bipartisan bill without further delay."
The rescue package was also Topic A on the presidential campaign trail.
"The first thing I would do is say, 'Let's not call it a bailout. Let's call it a rescue,"' McCain told CNN. He said, "Americans are frightened right now" and political leaders must give them an immediate solution and a longer-term approach to the problem.
Obama issued a statement saying that significantly increasing federal deposit insurance would help small businesses and make the U.S. banking system more secure as well as restore public confidence.
Sen. Hillary Rodham Clinton, who narrowly lost the Democratic nomination to Obama, said the Senate may have to lead the way in passing a rescue package. But other senators seemed inclined to let the House work out its problems first.
The bill's defeat came despite furious personal lobbying by Bush and support from House leaders of both parties. But the legislation was highly unpopular with the public; ideological groups on the left and the right organized against it, and Bush no longer wielded the influence to leverage tough votes. Even pressure in favor of the bill from some of the biggest special interests in Washington, including the U.S. Chamber of Commerce and the National Association of Realtors, could not sway enough votes.
The legislation the administration promoted would have allowed the government to buy bad mortgages and other deficient assets held by troubled financial institutions. If successful, advocates of the plan believed, it would have helped lift a major weight off the already sputtering national economy.
Associated Press writers Tom Raum, Ben Feller, Andrew Taylor and Julie Hirschfeld Davis contributed to this report.