(CNN) Senate Minority Leader Chuck Schumer's high-profile push for witnesses to testify in the Senate's expected impeachment trial of President Donald Trump shifted attention and political pressure on Monday to a handful of Republican senators who have worked diligently to avoid the spotlight.

The disparate group's views on the trial are a concern to the White House and GOP leaders , who are worried some could break and vote with Democrats on key trial-related issues, sources tell CNN.

If four of them were to buck calls from GOP leaders for a short, witness-free trial, it could upend the process and create the kind of wild uncertainty Senate Majority Leader Mitch McConnell says he has been carefully "coordinating" to avoid in ongoing talks with top White House officials.

The group includes moderates up for reelection, like Sen. Susan Collins of Maine, who may want to show independence from Trump; seasoned veterans, like Sen. Lamar Alexander of Tennessee, who are retiring and who may not feel politically bound to support the President; and outright critics of Trump, like Sen. Mitt Romney of Utah, who have challenged his unorthodox presidency and who may want to learn more about the allegations of a quid pro quo with Ukraine that is at the heart of the impeachment.

The group isn't big enough to threaten Trump's presidency -- there would have to be at least 20 Republicans break with Trump to provide the 67 votes needed to actually remove him from office and no one is predicting that. But if enough peel off they could provide Democrats with the 51 votes needed for key wins, such as to compel witnesses, demand documents and push through other procedural motions Democrats may seek during a trial.

McConnell is working to avoid surprises like that, but short of a reaching a broad agreement in negotiations with Schumer outlining the rules of a trial, he has said the twists and turns of a trial could be decided by 51 votes. Republicans hold a 53-47 seat majority, meaning just four Republicans voting with Democrats could have a major impact.

In addition to Collins, the list includes Sen. Cory Gardner of Colorado. Both are up for reelection in purple states and need to balance appealing to independent voters in their states without angering Trump supporters who they can't win without.

In addition to Alexander there are concerns about Sens. Pat Roberts of Kansas and Mike Enzi of Wyoming, both of whom are retiring committee chairman from the establishment wing of their party with rank and influence.

Sen. Lisa Murkowski of Alaska has defied Trump and the GOP by opposing the repeal of the Affordable Care Act and voting against Brett Kavanaugh for the Supreme Court.

Romney is perhaps the Senate's most outspoken Republican critic of the President. Trump recently called him a "pompous 'ass' who has been fighting me from the beginning," a gesture that may not promote loyalty from Romney who not long ago was his party's presidential nominee.

There are others who could break on some questions. Like Sen. Ben Sasse of Nebraska and Sen. Joni Ernst of Iowa, who have both been critical of Trump for various things he's done or said (especially about tariffs) despite Trump being popular in their states, and Sen. Martha McSally of Arizona who is up for reelection in a state trending purple.

At a news conference, Schumer tried to ramp up the pressure on this group of Republicans by saying he expects bipartisan support for his call for witnesses to testify.

"I expect to have the support of Democrats and Republicans because the arguments are so strong. And many Republicans have voiced to me and my colleagues privately that they think what the President did is wrong but they're just not sure enough facts have been presented to make the impeachable case. High crimes and misdemeanors. This is the way to do it," Schumer said.

Despite hand-wringing over the senators at both ends of Pennsylvania Avenue, there has not been much evidence yet any of them will break. Many are refusing to answer questions now that they are preparing to be jurors, making it hard to assess how deeply concerned they are about the allegations against Trump.

Asked if he was preparing to be an impartial juror, Enzi replied, "I'm not answering any questions on impeachment."

Alexander repeatedly gave a similar response when asked about a trial. But on Monday, he said, "We have a constitutional responsibility to have a fair trial and be impartial in our decision making and it would help if the two leaders could agree on what the procedure should be."

Romney said he would give Schumer's proposal for witnesses "good consideration" but wouldn't say if he what he would support.

"It's not that I don't have any point of view, it's just that I'm not willing to share that point of view till I've had the chance to talk to others and get their perspectives and when I do have something for you I'll get back to you," he told CNN.

Collins was critical of Schumer and McConnell. She said it was "unfortunate" Schumer released his letter publicly before engaging in private negotiations with McConnell and she said McConnell should not have signaled he was coordinating with the White House.

"Every senator has to decide on his or her own how to approach it. That would not be the approach that I've taken," she said of McConnell. "The only people I've consulted with thus far are the experts from the Congressional Research Service and I sat down with them for a session last week."

McSally had "no comment," when asked about impeachment.

Ernst on Monday didn't sound like she was going to break with Trump when she signaled she is not interested in an impeachment trial with witnesses, telling reporters "the shorter the better."

"This is a political exercise," Ernst said. "Let's just get it over with."