WASHINGTON -- Senate Republicans filibustered a package of tax breaks that most of them want Thursday, saying they were mad because Senate Majority Leader Harry Reid (D-Nev.) wouldn't let them vote on more tax legislation, which included an anti-Obamacare measure.

The Senate was considering a bill to temporarily extend some 60 expired tax breaks at a cost of about $85 billion.

Republicans favor the bill, which many voted for when it was crafted with a half-dozen GOP amendments in the Senate Finance Committee, but insisted they should be able to amend the bill further during floor debate.

Senate Minority Leader Mitch McConnell (R-Ky.) asked Reid to make the first of those amendments a repeal of the medical device tax in the Affordable Care Act, and then to allow alternating amendments from both sides.

But even as he asked, he suspected the answer would be no.

"This is completely out of control," McConnell said. "Even if the Democratic majority doesn't like our ideas or those of our constituents ... the answer isn't to shut down their representatives' ability to influence legislation through amendment."

Reid did object, however, arguing that the measure was already bipartisan and that the GOP just wanted to slow down the process.

"Everyone listen," Reid said. "The self-proclaimed guardian of gridlock just gave his presentation. That's what the Republican leader calls himself, and that is a good name he got for himself. That's what we've had here for five and a half years."

Although the bill failed for the time being, it is likely to be brought back up because of its broad popularity.

"We've got to get rid of these procedural issues on every bill," said Sen. Orrin Hatch (Utah), the top Republican on the Finance Committee. "This is a bill that virtually everybody in this body wants, to a more or less degree. Some want it very, very much."

The measure may have to wait until after the House passes similar legislation.