Republican senators emerged from a caucus meeting Tuesday voicing confidence they will win a vote later this week that would block new witnesses from being called and end President Trump's impeachment trial this week.

While Republican sources acknowledged several senators are wrestling with the question of whether to bring in former national security adviser John Bolton as a witness, they said Democrats do not have the four GOP votes they need to win such a vote.

While it does not appear that Republicans have the votes to reject such a motion yet, GOP senators on Tuesday said they thought the caucus would get there.

"We've been 100 percent united in this process to this point and it would be my hope that we can remain that way," said Sen. Kevin Cramer (R-N.D.).

He said Republicans will have at least the 50 votes they need to defeat the motion on witnesses.

"It's either going to be 53, 52 or 51, some number that starts with five would be my guess would be the vote to not have witnesses," Cramer said.

Sen. Lindsey Graham (R-S.C.) also voiced confidence.

"I feel good. I feel good that we're in a good spot," he said, "in terms of ending the trial sooner rather than later."

Sen. John Thune (S.D.), the chamber's No. 2 Republican, also expressed confidence, saying the trial shouldn't go past Friday.

The Tuesday meeting, held after Trump's defense team closed its impeachment case, using only 11 of its 24 hours in process, was an effort by Senate Majority Leader Mitch McConnell (R-Ky.) to persuade his colleagues to unify on the issue.

Republican senators described the special meeting as an effort to shore up the small group of GOP colleagues who might be willing to join Democrats in calling for testimony from Bolton or other witnesses.

One weapon McConnell and GOP leaders are using in their argument to try to persuade colleagues against voting for Bolton's testimony is Sen. Charles Schumer (D-N.Y.). They say agreeing to witnesses could give the minority leader carte blanche to force additional votes on subpoenaing more witnesses and documents, sources say.

During the meeting a handful of Republicans voiced concern about the public fallout of an unpublished book manuscript by Bolton that claims Trump told his former aide that he wanted to freeze military aid for Ukraine until Ukrainian officials announced an investigation of former Vice President Joe Biden, an assertion that goes to the heart of the Democrats' case against Trump.

Only two Republicans, Sens. Mitt Romney (Utah) and Susan Collins (Maine), say they will vote to consider motions to subpoena additional witnesses and documents. McConnell has prevented further defections.

But several other Republicans are on the fence.

Sen. Lamar Alexander (R-Tenn.) told reporters after the meeting that he will wait until senators have used their 16 hours of allotted time to ask questions before making a decision.

"I think the path forward is we got two days of questions and answers. That will take Wednesday and Thursday, and as far as I'm concerned after I finish hearing the answers to the questions and consider the record - I've now heard the arguments of both sides - then I'll make a decision about whether we need more evidence," he said.

Under the organizing resolution passed by all 53 GOP senators last week, the Senate is set to vote Friday on "whether it shall be in order to consider and debate under the impeachment rules any motion to subpoena witnesses or documents."

If the measure wins fewer than 50 votes, it will fail and the Senate will move to vote "yes" or "no" on the two articles of impeachment passed by the House.

If it gets 51 votes, the Senate will embark on an open-ended debate during which Schumer can force a litany of votes on witnesses and documents, as he did on Tuesday and Wednesday of last week when he kept the Senate voting past 2 a.m.

Republican senators are worried that Schumer will painfully drag out the process if they vote to consider additional witnesses, and not just settle for hearing from Bolton, according to two GOP lawmakers familiar with internal conference discussions.

In the case of a 50-50 tie, there's a possibility that Supreme Court Chief Justice John Roberts could step in and rule in favor of witnesses.

Schumer on Tuesday said he would like to see Roberts rule in favor of witnesses, arguing that the weight of his opinion would convince enough Republicans to go along with it. Other Democrats say Roberts should break a 50-50 tie. But either move would be seen as highly political and polarizing - a reason Roberts might choose to avoid either step.

Republicans are also looking for ways that would make it easier for them to not vote for Bolton's testimony.

One proposal garnering buzz came from Sen. James Lankford (R-Okla.), who said he was in negotiations with the White House to make Bolton's unpublished manuscript available for senators to read in a classified setting. The National Security Council is currently reviewing the draft to make sure it doesn't include classified information.

By keeping the manuscript in Congress's sensitive compartmented information facility, senators can read it before it's fully declassified.

Democrats have scoffed at that idea, and Republicans aren't fully on board with the proposal.

"I don't know," Sen. Lisa Murkowski (R-Alaska), a pivotal swing vote, said Tuesday afternoon when asked about Lankford's proposal.

"Is it looking at the whole manuscript? Is it just isolated references? If it's classified, how can we gain access to it? What can we say about it? It's an idea that's been presented. I just don't know," she said.

Sen. Pat Toomey (R-Pa.) is pushing for a swap of witness testimony, whereby the House managers would have a chance to seek testimony from Bolton and Trump's lawyers would be able to ask questions of Biden's son Hunter Biden.

But McConnell hasn't yet signed onto the idea and would prefer to avoid subpoenaing new witnesses and risking a battle over executive privilege that could extend the trial indefinitely.

Another proposal floated by Republican senators Tuesday afternoon was to give Roberts "a more elevated" role so that he could perhaps make a ruling to hear from Bolton but not additional witnesses, according to a lawmaker in the room.

McConnell warned wavering Republicans at a lunch meeting earlier Tuesday that if they vote to bring in new witnesses it could extend the trial for weeks and would inevitably result in Trump's acquittal.

He cautioned colleagues that opening up the trial to new evidence could take it in unpredictable directions for an unknown amount of time, eating up the Senate calendar.

The GOP leader told undecided colleagues to "sort through this to look at the information" and "look at the big picture in terms of what this means," said Sen. Mike Braun (R-Ind.).

If four Republicans vote to subpoena new evidence, it would be a major political victory for Schumer, who has made the debate more about seeking damaging information about Trump than actually removing him from office.

Sixty-seven votes are needed to convict Trump on articles of impeachment passed by the House, and Democrats acknowledge they're nowhere close to having enough support to do that.