But Senator Harry Reid, Democrat of Nevada, who is the majority leader, said Thursday night that it was his understanding the House would join in the Senate approach.  Senator Kent Conrad, Democrat of North Dakota, who is the chairman of the Budget Committee, opposed the Senate plan, saying that while it was proper to limit the reach of the tax, it was wrong to do so without replacing the money. “It ought to be paid for,” Mr. Conrad said. “The revenue ought to be replaced by spending cuts or other revenue.”  Republicans, who say Democrats should have addressed the alternative tax issue months ago, have repeatedly objected to efforts to compensate for changing the tax provisions. They argue that since the tax was not intended to produce such high levels of revenue when it was created, the money should not have to be replaced.  “They are all phantom funds,” said Senator Judd Gregg of New Hampshire, the senior Republican on the Budget Committee, referring to the revenue that would be generated by the tax.  Earlier Thursday, Republicans banded together to prevent the Senate from considering the House bill. That led to the later vote, in the Senate, on freezing the alternative minimum tax, which sent that proposal back to the House.  The alternative minimum tax was created almost 40 years ago to prevent affluent Americans with numerous deductions from escaping income taxes. But since it was not tied to inflation, it is reaching more and more people.  Experts say the tax cuts approved in the early days of the Bush administration have also pushed more people under the tax. The Treasury Department estimates that without a change in law, a total of 23 million people would have to pay the alternative tax on their 2006 taxes, at an average of about $2,000 each. The tax could reach some Americans earning $50,000 or even less.  Mr. Reid said that he supported the “pay-go” concept embraced by Democrats but that he was left with few options because of the Republican ability to block any alternative minimum tax relief that complied with such budget rules.  “We’ve tried every alternative possible to do this,” Mr. Reid said. “I believe in pay-go. I think that’s where we should be.”  A version of this article appears in print on , on Page A18 of the New York edition with the headline: Senate Backs Freeze on Tax Without Cost Offsets. Order Reprints| Today's Paper|Subscribe
The Senate on Thursday voted overwhelmingly to prevent the alternative minimum tax from hitting millions of middle-class Americans without replacing the $50 billion that would be lost.