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Senate Majority Leader Mitch McConnell, R-Ky., said Tuesday he has enough Republican votes to start the impeachment trial of President Donald Trump without the support of Democrats, who have been demanding witness testimony.

But his announcement doesn't settle the contentious issue of whether witnesses will be allowed to testify during the Senate trial — which Democrats have called for. Rather, it postpones a vote on the issue — leaving open the possibility that a handful of Senate Republicans could break with the party and back Democratic efforts to call witnesses against the president.

The announcement by McConnell means that the trial would begin once House Speaker Nancy Pelosi, D-Calif., transmits the two articles of impeachment — alleging abuse of power and obstruction of Congress — to the Senate. Under McConnell's rules, the question of whether witnesses would be called would be dealt with later in the trial.

The first phase of the trial would include "arguments from the prosecution, arguments from the defense" and a "period of written questions" submitted by senators of both parties, McConnell said.

Only after that phase would "the issue of calling witnesses" be addressed, as it was during President Bill Clinton's impeachment trial 20 years ago.

"That will be addressed at that time and not before the trial begins," he said.

McConnell said throughout the House impeachment process that he wants the Senate trial to follow the precedent set in Clinton's trial. Then, there was a two-step process: an initial agreement to first hear the prosecution and the defense arguments and, later, a vote on whether to have witnesses.

Senate Minority Leader Chuck Schumer, D-N.Y., has said he wants a single resolution at the start that would set the parameters for the trial and allow for calling new witnesses. The potential witnesses sought by Democrats include former national security adviser John Bolton, who said Monday that he would be willing to testify if subpoenaed, and acting White House chief of staff Mick Mulvaney.

When the trial kicks off, a simple majority of senators will be needed to pass procedural matters, including the question of witness testimony. (Sixty-seven votes are needed to convict and remove a president.)

Republicans have a 53-47 majority in the Senate, meaning Democrats would need four Republicans to join them in seeking to compel Bolton and others to testify.

These are the four GOP senators who are being most closely watched as those who could split from Republicans.

Mitt Romney of Utah

Romney, who is Trump's most outspoken Republican critic in the Senate, has made no secret of his desire for a more complete process.

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He (along with Republican Sens. Susan Collins of Maine and Lisa Murkowski of Alaska) refused in October to add his name to a resolution condemning the House impeachment inquiry.

And he told reporters Monday that Bolton should testify. "Sure, I'd love to hear what he has to say," Romney said.

On Tuesday, Romney said he was "comfortable" with the Clinton trial model sought by McConnell and added that the approach could "accommodate" Bolton's testifying.

Susan Collins of Maine

Collins, unlike Romney, faces a tough re-election effort in her blue-hued state, complicating her approach toward impeachment.

Collins needs to pull votes from both parts of her state — the Democratic-leaning coast and the conservative-leaning interior. But she risks angering both groups: the Republican base by not taking a hard line in support of acquittal and Democratic voters by not taking a hard line against it.

Collins — who last month criticized McConnell, saying it was "inappropriate" for the majority leader to coordinate Trump's defense with the White House — has said repeatedly that she can't take a position on impeachment because she would essentially be serving as a juror during a trial, and she has criticized Republicans and Democrats alike commenting on the trial before it has even started.

But on Monday, she said she would support McConnell's position — but she added that there are a "number of witnesses that may well be appropriate."

Lisa Murkowski of Alaska

Murkowski said in an interview on Christmas Eve that she was "disturbed" that McConnell would engage in "total coordination" with the White House regarding the trial.

In a brief interview with NBC News on Monday, Murkowski avoided answering questions about Bolton's testifying, saying only, "I want to get to the first step" — a reference to the Senate's receiving the articles of impeachment.

She added that she supported McConnell's position on the structure of the trial.

But Murkowski hasn't been reluctant to buck her party: She voted against the Trump-backed effort to repeal Obamacare in 2017 and against the confirmation of Supreme Court nominee Brett Kavanaugh.

Cory Gardner of Colorado

Gardner, who is up for re-election in a state , is perhaps the most vulnerable GOP senator in 2020, making his approach on impeachment unpredictable.

In October, he refused to say whether it was inappropriate for Trump to ask a foreign power to investigate a political rival.

Then, last week, in response to questions from The Denver Post about whether the president's Cabinet members should testify, Gardner released a statement avoiding answering the question and instead criticized Pelosi, saying her impeachment inquiry was a "total circus that has only served to divide this country."

In a brief interview with NBC News on Monday, he wouldn't answer questions about whether he wanted Bolton to testify, replying, "I know you guys want to have a trial by Twitter, but is Nancy Pelosi going to follow the Constitution?"

Trump remains unpopular in Colorado. According to a poll last month by Morning Consult, 57 percent of registered voters in the state said they disapprove of the job he is doing as president, while just 39 percent said they approve. Meanwhile, 54 percent said they supported the impeachment inquiry in a poll in October.

Others ...

A couple of more Republican senators have signaled, subtly, that they could be open to breaking from their party on some trial matters, such as witnesses.

Joni Ernst of Iowa, who, like Collins and Gardner, is facing a tough 2020 re-election, said Monday that it was "yet to be determined" when she was asked whether she wanted Bolton to testify.

Shelley Moore Capito of West Virginia was also noncommittal, saying the Senate should decide on whether Bolton should testify later in the trial.

Asked whether she would vote to subpoena Bolton, Moore Capito replied, "I can't say that yet."