Senate Majority Leader Harry Reid, D-Nev., said he expected the administration and the Fed to have a proposal to lawmakers in a matter of hours, rather than days.
Paulson, Bernanke and Securities and Exchange Commission chair Christopher Cox asked lawmakers at the session to act swiftly in passing legislation.
"It will be the power -- it may not be a new entity -- it will be the power to buy up illiquid assets," Rep. Barney Frank, D-Mass, said.
"There is this concern that if you had to wait to set up an entity, it could take too long," Frank said.
Frank said there was "virtually unanimous agreement" among lawmakers in attendance of the need for such action and that the House Financial Services Committee, which he chairs, could have a legislative drafting session on a proposal as early as Wednesday
Stocks rallied more than 400 points late Thursday after a report that the Bush administration was working on a new plan to alleviate fallout from the housing and credit crises. Those debacles have badly bruised the economy and pushed unemployment to a five-year high.
"What we are working on now is an approach to deal with the systemic risk and the stresses in our capital markets," Paulson said.
"The root cause of the stress in the capital markets is the real estate correction," he added.
Bernanke said he looked forward to working closely with Congress to "resolve this financial crisis and get our economy moving again."
President Bush canceled an out-of-town trip Thursday to stay in Washington and meet for 40 minutes with Bernanke, Paulson and Cox, along with White House and Treasury Department aides.
Rep. Nancy Pelosi, D-Calif., said any potential action must protect taxpayers who are already on the hook for potentially billions of dollars in bailouts to financial firms taken down by the financial crisis.
Once Congress gets the administration's proposal, Pelosi said: "We hope to move very quickly. Time is of the essence."
Pelosi wrote to Bush on Thursday saying Congress would meet beyond its planned Sept. 26 adjournment, if necessary, "to consider legislative proposals and conduct necessary investigations" related to the financial crisis.
Administration officials said it was critical that Congress act next week, according to sources familiar with the meeting, who spoke on condition of anonymity because it was private.
Frank suggested Democrats might try to tie the authority to additional steps to help struggling borrowers keep their homes.
Republican leaders said any attempt to use the administration's request for leverage on other priorities would be inappropriate.
"Now is not the time to seek political leverage or a quid pro quo," said Reps. John A. Boehner of Ohio and Roy Blunt of Missouri, the top two House Republicans, in a statement.
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