Senate Democrats succeeded on Wednesday at ending debate on a bill that would extend most Americans' jobless benefits by at least 14 weeks.

The 97-1 cloture vote concludes a four-week standoff between the majority party and GOP leaders over the extension, a version of which passed the House in September.

Democrats now expect a final vote on the substance of the bill to take place late Thursday.

"Almost 2 million Americans [are about to lose their jobless benefits], and we've been trying to pass an extension of unemployment insurance for the past month," said Sen. Jeanne Shaheen (D-N.H.), one of the bill's chief proponents, after the vote.

"This broad, bipartisan vote acknowledges unemployment affects every community, every state, every part of our country," she added on the floor, noting that previous, similarly bipartisan votes to advance the bill have hardly expedited its progress.

Despite Wednesday's procedural vote, some Senate Republicans remain unhappy with the bill, primarily because Democrats prohibited them throughout the debate process from offering a series of amendments they said were essential.

The party initially proposed nine revisions, including one that targeted immigration verification rules and another that would have changed a portion of the Troubled Asset Relief Program (TARP). But Democratic opposition inevitably forced Republicans to limit their amendments to only three.

Foremost among those remaining amendments was an edit that would have required Congress to pay for its unemployment insurance extension using unspent TARP money, rather than through an extension of an unemployment tax levied on employers. Both the House and Senate versions of the bill contain that funding mechanism.

But those proposals also never reached the floor, which angered Senate Republicans. They insisted the chamber could have wrapped up debate and approved the extension last week, one GOP aide stressed Wednesday before the vote. 

"They are only trying to delay and stall things," Senate Majority Leader Harry Reid (D-Nev.) said of the GOP's criticism on Tuesday, before Democrats called for cloture. "We have done more legislating on voting on non-germane, non-relevant amendments this Congress I think than any time in the history that I've been around. And we've done it because the Republicans said that's what they wanted, and I wanted to be fair."

Democrats did, however, add to their bill an extension of a first-time homebuyers tax credit, which top Republicans do support. 

[UPDATE: Democrats now plan to vote on the unemployment extension this afternoon.]