On the Senate side, there were similar demands for some changes in Paulson's bailout blueprint.
Senate Banking Committee Chairman Sen. Chris Dodd, D-Conn., said there must be oversight, and he wants to structure the package to ensure that taxpayers are the first to be paid back "once conditions in the industry stabilize and recover."
He added that "the last thing any of us want is to be back here in a month coming up with some new plan because this didn't work. It's important that we act quickly, but it's more important that we act responsibly."
Some in the financial world are also lobbying for changes. They want the bailout to be expanded beyond banks to cover other financial services industries, and are arguing against Democratic efforts to reduce mortgage rates for those facing foreclosure.
Despite Paulson's alarming scenario described on Sunday morning news shows, by the end of the weekend, political opposition was growing.
Sen. John McCain, the Republican presidential candidate who recently said the fundamentals of the economy were strong, told NBC's "Today" show, "We are in the most serious crisis since World War II."
Earlier McCain said he would insist on an oversight board because he is "greatly concerned that the plan gives a single individual the unprecedented power to spend $1 trillion on the basis of not much more than "Trust me."
He suggested candidates for the board, such as billionaire financier Warren Buffett, former Massachusetts Gov. Mitt Romney and New York City Mayor Michael Bloomberg.
McCain also said that the final deal must make sure that taxpayer cash did not pay for bonuses to executives whose firms had to be rescued.
One executive actually rejected his bonus.
Shareholders of the giant insurance company American International Group, which was given a $85 billion government lifeline last week, were scheduled to meet Monday.
AIG's fired CEO Robert Willumstad informed the company that he would not accept the $22 million severance payment that was part of his contract, The Wall Street Journal reported.
Despite the objections, House Speaker Nancy Pelosi predicted Congress would pass a package this week.
ABC's Ann W. Compton, Jake Tapper, George Stephanopolous and Alice Gomstyn contributed to this report.