WASHINGTON (CNN) -- A small group of Democratic House members put together an alternative to the $700 billion financial bailout measure that was defeated in the House on Monday.
Rep. Peter DeFazio, D-Oregon, said they tentatively are calling their options the "no bailouts act," which would eliminate or reduce the risks to taxpayers in bailing out financial institutions holding bad mortgage assets.
The group introduced its bill after the House on Monday rejected a $700 billion bill that would have authorized Treasury Secretary Henry Paulson to buy bad mortgage-related securities and other assets that have been clogging credit markets worldwide.
DeFazio said he voted against Monday's bill because taxpayer protection measures were "nonexistent."
"I have very little confidence in Mr. Paulson," DeFazio said at a news conference with several other House members, who want Wall Street, not taxpayers, to bear the burden of the bailout.
DeFazio said the crisis can be resolved with market discipline and regulatory functions, which would open up lending opportunities for banks and other institutions.
After the House defeated the administration-backed bailout package 228-205, the stock market dove 778 points, which represented more than a trillion dollars in losses. See more about the bailout plan »
Administration officials, as well as Federal Reserve Chairman Ben Bernanke and the bipartisan congressional leadership, have warned that a financial rescue package must pass quickly to head off a credit crisis that could undermine the nation's economy.
But members of the Democratic group offering the alternative measure said they were pressured to act too quickly.
"The whole bill has been fueled by fear, and hinged on haste," Rep. Lloyd Doggett of Texas said at a news conference Tuesday.
Rep. Elijah Cummings, D-Maryland, added, "I think every single member of Congress understands the urgency of this matter and we all want to resolve it, but ladies and gents, let me be clear: Just because we have an urgent situation doesn't mean we don't have to be deliberative."
The group offered its alternative act after Senate leaders pleaded for an end to the finger-pointing that erupted after the collapse of the financial rescue plan Monday.
House Democrats and Republicans immediately blamed each other for the bill's defeat.
Republicans accused House Speaker Nancy Pelosi of being overly partisan before the vote, but Democrats said the Republican leadership failed to deliver the votes they promised, as Republican members voted by a ratio of more than 2 to 1 against the bailout.
And in fact several House Republicans, including Minority Whip Roy Blunt of Missouri and Michelle Bachmann of Minnesota, later admitted that the GOP members voted against the bill because they opposed it.
We are not babies, sucking our thumbs," Bachmann said.
But on Tuesday, both the top Democrat and the top Republican in the Senate said they were confident they could pass a rescue plan with bipartisan support despite the partisan bickering on the other side of the Capitol. Watch a debate on whether the bailout is a good idea »
"The blame game needs to end, and we need to move forward on doing what's right for our country," Senate Majority Leader Harry Reid, D-Nevada, said on the Senate floor.
"I am hopeful and I am confident that all sides -- House and Senate, White House -- will work together to achieve a goal that will be good for the American people," Reid said.
The Senate plans to vote on the $700 billion bank rescue plan Wednesday evening.
The bill adds provisions -- include raising the FDIC insurance cap from $100,000 to $250,000 -- and will be attached to an existing revenue bill, according to several Democratic leadership aides.
The vote is scheduled for after sundown, in observance of the Jewish holiday.
Senate Minority Leader Mitch McConnell, the top Republican in the Senate, said earlier that he thought Congress would pass a financial rescue package this week.
"This is not the time to fix the blame. This is the time to fix the problem. ... We will reassure the American people that Congress can rise to the occasion, act like grown-ups, if you will, and get the job done for all of our people," the Kentucky senator said.
On Tuesday, Reid and Pelosi sent a letter to President Bush reiterating their support for a bipartisan bailout plan.
The Democratic leaders said that the defeat of the bailout "resulted in additional severe economic impacts both on Wall Street and on Main Street" and that they were "committed to working with you and our Republican colleagues to enact a bipartisan bill without further delay."
CNN's Lesa Jansen and Scott J. Anderson contributed to this report.