Updated

The House on Wednesday passed a one-year fix to the alternative minimum tax, preventing some 20 million more U.S. taxpayers from being subject to a tax hike, but the measure did not find ways to pay for the estimated $50 billion in lost revenues created by the patch.

The bill passed on a vote of 352-64, and now heads to President Bush's desk for his signature, and he has indicated he would sign it.

Earlier Wednesday, a key House bloc of fiscally conservative Democrats — who were angered over the handling of legislation to fix the AMT — backed off its threat to hold Congress hostage over the winter break, giving the bill a needed boost.

The version the House passed had cleared the Senate Tuesday night. The tax initially was aimed at the richest Americans but was not pegged for inflation, so it has steadily included more and more taxpayers. Without a permanent change to the law, Congress must act every year to stem the AMT's creep into more tax filings.

The Blue Dog Democrats — 47 House members who stand on a fiscally conservative platform —favored a fix, but they wanted it to be paid for. The Blue Dogs advocate pay-as-you-go spending that requires any increases in spending to be paid for with increases in revenue.

To get what they wanted, the Blue Dogs had threatened to vote in opposition of the version of the patch that the Senate passed, as well as possibly garner enough votes to prevent the House from adjourning for its holiday recess.

But Wednesday, Blue Dog Rep. Mike Ross, D-Ark. — who has been leading the charge on the AMT issue — said that in the end, they he believes that fighting the bill and keeping the House in session through the holidays would punish no one except staff.

"The whole situation is very frustrating to us," Ross said, refraining from criticizing House Democratic leaders.

"They hung tough I think. They hung with the Blue Dogs to the very end. They had to go for paying for it (the AMT) or not covering 20 million people. Our regret as Blue Dogs is that we couldn't give them both," Ross said.

Senate Republicans blocked the Senate from taking up legislation that includes a tax increase, and Bush threatened to veto any bill that raised taxes.

On Tuesday night the Senate for a second time rejected the House-backed approach of a paid-for AMT bill. The House Democratic leadership, which was committed to paying for the tax relief, had asked the Senate to make one last stab at the issue. The Senate vote was 48-46 for the House bill, 12 short of the 60 needed to approve it.

With that vote, the House had no choice but to take up the Senate bill, which shields some 21 million taxpayers without a means to cover the cost to the Treasury.

"Let me be clear, there is no disagreement between Republicans and Democrats over protecting the middle class from the AMT," House Majority Leader Steny Hoyer, D-Md., said. "The question is, will we do so responsibly or charge tens of billions of dollars to our grandchildren?"

The AMT was created in 1969 to make sure that a small group of very rich people did not totally avoid paying taxes. But the tax, which applies more stringent rules for using deductions in calculating tax obligations, was never adjusted for inflation, and every year more middle- and upper-middle-level income people are hit by the tax.

Congress has responded by passing annual fixes, or patches, to keep the AMT from affecting more people. Without a fix, taxpayers subject to the tax could grow from 4 million in 2006 to 25 million this year.

Even with House passage of an unpaid-for bill, the consequences of the congressional dispute could be felt by millions.

The Internal Revenue Service has said that it will take seven weeks from the time the bill is signed into law to reprogram and test forms, going well past the planned mid-January start of the 2008 filing season.

The IRS said Tuesday that it has yet to decide whether certain delays in processing returns and sending out refunds will affect AMT taxpayers or all taxpayers.

FOX News' Chad Pergram and The Associated Press contributed to this report.