A Senate deal to move forward on legislation that would shield millions of taxpayers from the Alternative Minimum Tax (AMT) and extend a package of expiring tax breaks collapsed on Tuesday amid Republican objections to tax increases attached to the bill.

Citing disappointment with the Republican opposition, Senate Majority Leader Harry Reid (D-Nev.) filed cloture Tuesday to proceed to a vote on Thursday on House legislation to patch the AMT.

At press time, it seemed unlikely that any compromise would be revived before the Senate broke for the evening, but Senate Finance Committee Chairman Max Baucus (D-Mont.) expressed hope that the two parties could reach an agreement.

“There may be the beginnings of something here and I hope that’s the case,” he said in response to a description of the Republican proposal by Minority Leader Mitch McConnell (Ky.).

Both Republicans and Democrats are under pressure to pass AMT relief by the end of the year. If Congress does not act, roughly 19 million additional taxpayers will get hit by the tax next spring.

Under the proposal from Senate Democrats, AMT relief would be extended for one year without offsets, while the expiring tax breaks would be extended for two years. Known as the “extenders,” the tax breaks would be offset with three provisions raising taxes on businesses, including private equity firms that go public.

Sen. Jon Kyl (Ariz.), the chairman of the GOP Senate conference, indicated there wasn’t much support among Republicans to offset the extenders. “It makes no sense to use a permanent tax increase to offset a temporary extension [of tax relief].”

He also indicated that Republicans would object to a particular provision that would tax all publicly traded investment partnerships as corporations. “My guess is you’d see quite a lot of opposition,” Kyl said.

Reid told reporters Tuesday morning that he and McConnell had struck an agreement that would have prompted Reid to send a unanimous-consent request on the Democratic proposal on Tuesday.

But the deal fell through, partly because of objections from the business lobby over one of the pay-fors.

“I thought we would have that worked out, based on a conversation I had with Sen. McConnell this morning, but obviously he’s had some problems since then,” Reid said on the floor.

The provision would have limited the number of years businesses could use current-year losses to offset previous years’ tax liabilities. Lobbyists said they weighed in against the measure to GOP leadership aides on Tuesday.

By not acting on AMT relief sooner, Congress may have disrupted the tax-filing season. U.S. Treasury Secretary Henry Paulson warned in a letter to lawmakers in October that the enactment of an AMT patch in December could delay the tax returns of as many as 50 million filers, slowing the issuance of as much as $75 billion in refunds.