The Senate is driving toward a climactic and dramatic vote at 1 a.m. Sunday that could determine whether a bipartisan deal to raise the nation’s legal borrowing limit is possible or a government default is likely.

What that deal might look like was still deeply uncertain Friday, but talks were underway between Democrats and Republicans in the Senate about methods to circumvent some of the chamber’s most cumbersome procedures to allow the Senate to act more quickly if a compromise is reached.

Speedier action would require unanimous agreement from all senators, including conservatives who have vowed not to raise the debt ceiling without congressional approval of a balanced budget amendment to the constitution, and it wasn’t clear that would be forthcoming.

On Friday evening, the Senate rejected a proposal to raise the debt limit for a few months that emerged from the House after days of intra-party fighting among House Republicans.

Senators instead moved forward with an alternative advanced by Majority Leader Harry M. Reid (D-Nev.), which would raise the debt ceiling through the 2012 election, but they hoped to amend the bill in coming days if a bipartisan compromise is reached.

Now, Senate rules require a full day in between Reid introducing the measure Friday night and a vote to cut off debate, leading to a key vote early Sunday.

Closing debate will require the approval of 60 senators, meaning Reid will require at least seven Republican votes to clear that hurdle.

If the measure cleared that hurdle, the final passage would require a simple majority of senators to send the bill to the House. Without unanimous agreement, however, it would require an additional 30 hours of debate for that final vote, meaning 7:30 a.m. Monday would be the earliest a final vote could happen.

Then, the measure would return to the House on Monday, where it would face a final critical vote — with the outcome deeply uncertain, as world markets watch nervously.

Rank-and-file senators in both parties sounded increasingly conciliatory Friday, raising hopes that they could find agreement to ship a compromise to the House before the default deadline of Tuesday.

But it was not at all clear whether a majority could be found to support such a compromise in the House, where leaders had been almost entirely focused on wrangling GOP votes for House Speaker John A. Boehner’s proposal in recent days. Exhausted Republican House members said they had given little thought to what further compromises they might make.

Democrats in the Senate said they believed senators of both parties wanted to avoid a repeat of the experience of the House, which Friday passed a GOP bill from Boehner (Ohio) that would provide for a short-term increase in the legal debt limit. “I think there’s a great willingness to be bipartisan,” said Sen. Dianne Feinstein (D-Calif.) “We don’t want to replicate the House. We’d like to work together on something that will work for all of us.”

Republicans laid out terms — they want to be sure that Congress will be required to tackle entitlement and tax reform in coming months and cut deeply from debt, even if the legal borrowing limit is allowed to rise through the 2012 election, as Democrats have demanded.

But they also noted that elements of Boehner’s bill are strikingly similar to Reid’s.

Both plans cut some spending now and then establish a congressional committee charged with slashing $1.8 trillion from the deficit.

“The truth is, they weren’t that far apart,” said Sen. John Thune (R-S.D.) “I think if you look at the basic framework, it wouldn’t be that hard to figure out something that we could perhaps agree upon.”

Only Boehner’s plan required that Congress adopt the committee’s recommendations before the debt ceiling could rise again in the spring.

Even Sen. Jim DeMint (R-S.C.), who had promised to use all parliamentary procedures at his disposal to slow approval of any plan without a balanced-budget provision, said Friday that he was still mulling his strategy in coming days.

“I don’t know what I’m going to do,” he said, indicating he would take into account an appeal from McConnell to allow an expedited process, if a compromise was reached. “I’m certainly going to listen — we’re playing up against a pretty important deadline here, and I don’t want to fool with that.”