Republicans have rejected a request by Majority Leader Harry Reid (D-Nev.) that the Senate approve by unanimous consent a one-year patch to the Alternative Minimum Tax (AMT) with no accompanying tax increases.

Democrats quickly made political hay of the GOP move, which contradicted earlier Republican calls for extending tax relief with no offsets.

Sen. Judd Gregg (R-N.H.), speaking on behalf of Republicans, objected, but said he thought a deal could still be worked out “hopefully sooner rather than later.”

A GOP aide said Gregg objected to give senators time to consider the request.

Reid’s request came after Republicans blocked a procedural vote to debate an $81 billion  House-passed measure shielding millions from the AMT for one year and extending a package of popular tax breaks. The House bill included tax increases on businesses to pay for the tax relief.

Both Republicans and Democrats are under pressure to pass a one-year AMT patch this year, since if they fail 19 million filers will be hit by the creeping tax. The “extender” package is also considered must-pass legislation, though it’s not quite as urgent as the AMT.

The two parties disagree over whether to “pay for” the tax relief by attaching revenue offsets, with Democrats strongly preferring to stick with heir pay-go budget rules and Republicans balking at instituting any new axes to extend current relief.

After forcing Democrats to agree to a “clean” one-year AMT patch with no offsetting tax increases before the Thanksgiving break, Republicans then voiced opposition to offsetting the extenders. They also demanded votes on instituting a flat tax, permanently repealing the AMT and extending the Bush tax cuts.

Speaking on the Senate floor, Reid said he planned to request a vote on the one-year patch again later on Thursday afternoon.