Closed-door bipartisan immigration talks brought the Senate to a near standstill Tuesday as Democratic and GOP leaders sought to give negotiators as much flexibility as possible to complete work on a comprehensive reform package that could garner broad support.

With the immigration talks continuing into Tuesday night, Republicans said they hope the progress of the negotiations will help them convince Majority Leader Harry Reid (D-Nev.) to give them more time to work out the details and put pen to paper on a bill before forcing a vote today on proceeding to last year’s bill, as is expected.

Republicans were scheduled to have a full Conference meeting this morning in the Capitol to discuss the bill and determine how to proceed.

Sen. Mel Martinez (R-Fla.) said Tuesday evening that progress was being made on the details but staff needed to spend the coming hours drafting language to a prospective bill. Martinez said he was holding out hope that the cloture vote may be delayed a day or so to allow the text of a measure to come together.

“We’re not going to come out tonight and say we got a deal,” Martinez said, heading back into the closed-door talks. “But we are making progress.”

Sen. Arlen Specter (R-Pa.), the ranking member on the Judiciary Committee, agreed Tuesday night that progress was being made, but “there are still a few issues outstanding.” He added, “a lot of language has already been prepared” and more drafting is in the works, especially on some of the headier matters.

Asked about the timing of producing an agreement, Specter said: “We may have to spill over to tomorrow. I don’t think we can wrap it all up tonight.”

Conservative Republicans said they are uncomfortable agreeing to debate immigration reform before they see any actual bill language, while more moderate GOP Senators may not want to face the political fallout from blocking movement of a hot-button issue heading into 2008.

“It’s kind of a minefield,” conceded one GOP Senator. “There’s no unanimity” on how we move forward.

Reid has so far remained firm on his decision to hold a cloture vote on moving to last year’s immigration bill today. But a Democratic aide familiar with the issue said the Majority Leader has left enough flexibility in his handling of immigration to give negotiators several more hours — or even until Thursday morning — before finally forcing the issue.

For instance, Reid could put off the vote until later today, allowing talks to continue up to then. Or if a deal is imminent, Reid and Senate Minority Leader Mitch McConnell (R-Ky.) could look to broker a deal whereby cloture is invoked on the bill and then put it aside until Thursday, giving negotiators time to finish up their work while the Senate moves onto one of the other measures in the legislative pipeline.

For instance, while Reid and McConnell have reached a deal to move a placeholder Iraq War supplemental, the two leaders held off on announcing details of the plan Tuesday, although they did say they were committed to moving it off the Senate floor by Friday.

GOP Senators huddled Tuesday at their weekly policy luncheon to discuss immigration strategy, but both aides and Senators said no decisions were made on how to proceed. Republicans will convene again this morning to figure out how to approach the scheduled vote to move onto the issue — a meeting Senators said will center largely on the outcome of Tuesday night’s negotiations.

Heading into those talks Tuesday afternoon, Republicans saw at least 10 outstanding issues yet to be resolved. Wading through those could take hours or even days, some Senators said.

Senate Minority Whip Trent Lott (R-Miss.) said before the meeting, “It’s a lot more complicated an issue to deal with than people recognized.” With that in mind, Lott said Reid should consider giving the talks more time in order to produce a draft of a measure that Senators can review before considering it on the floor.

“I don’t think we ought to just go forward regardless,” Lott said. “If we do that, the wheels will just come off.”

But Lott also said he understands why Reid has thus far remained firm on his deadline and said he continues to believe Reid has done a good job of handling the thorny issue.

“I’ve defended Sen. Reid’s decision” to impose a deadline, Lott said Tuesday, explaining that the pressure often helps bring negotiators to an agreement. “Usually the main players have to get in a room and stay there until good sense or exhaustion wins out. And sometimes it’s a combination of both.”

Additionally, while he agreed it may be difficult for lawmakers to agree to begin floor debate if they do not have enough time to review the actual language, he downplayed the likelihood it would stall the effort. “Academically that’s a good thing … [but] I don’t think a lot of Senators are going to actually read the thing. So let’s get real here,” he said.

Democrats, meantime, said they want to keep the momentum going — believing that the more pressure put on the process, the greater the chances a bipartisan bill can come about before Memorial Day. Reid reiterated his plan to hold a procedural vote today that would allow debate to begin, a move that currently would bring up last year’s Senate immigration reform package that garnered 63 votes.

Before talks began again Tuesday afternoon, Reid expressed hope a deal was in reach: “There has been some accomplishments. Certainly we are a long ways from where we need to be, but there has been some accomplishments.”

Reid has said if and when the bipartisan talks bear fruit, he would use their immigration outline as a substitute to last year’s Senate bill.

That move worries some Republicans, who fear that if the talks fall apart, Reid will force a do-over on the Senate debate from last year, which even some moderate Republicans argue is no longer workable. At the same time, some GOP Senators don’t want to have to change their vote from last year and face the political fallout associated with switching their position.

On the other end of the spectrum, conservative Republicans are concerned that the discussions are tilting too far to the left and ultimately, when the bill goes to conference with the liberal-leaning House, it will be completely unpalatable.

Sen. John Cornyn (R-Texas.), one of the lead conservative negotiators, said early Tuesday he believed more time was needed before Senators would feel comfortable agreeing to debate a measure sight unseen. That’s especially true of those Republicans who have not been privy to the intimate bipartisan talks, which have been ongoing for weeks.

“We have a responsibility — each of us — to know what we’re voting on,” Cornyn argued. “So, things may have to get pushed back.”

Across the Capitol, House Majority Leader Steny Hoyer (D-Md.) told reporters Tuesday his chamber is still on track to bring an immigration bill to the floor in July, whether or not the Senate can move a bill.

“It is our expectation that we will have an immigration bill on the floor in July,” Hoyer said. “Now, could that change depending on what the Senate does? It could change, but at this point in time whether the Senate acts in the next day … or week will not necessarily impact that decision.”

A House GOP leadership aide said Democrats are still willing to bring a bill to the floor if the Senate fails to do so as long as Bush can deliver Republican votes. So far Congressional Democrats and the White House have been working closely to move a bill, and Rep. Zoe Lofgren (D-Calif.) is taking the lead on the issue.

“We’ve talked to the president about it, it’s one of the things we think we can work with the president on,” Hoyer said.

Susan Davis contributed to this report.