(CNN) A growing number of Republicans are pointing to President Donald Trump's threat to invoke executive privilege in order to make their case against subpoenas sought by Democrats for key witnesses and documents, a development that could bolster Senate Majority Leader Mitch McConnell's goal of a swift end to the impeachment trial.

GOP senators are privately and publicly raising concerns that issuing subpoenas -- to top officials like acting White House chief of staff Mick Mulvaney and former national security adviser John Bolton and for documents blocked by the White House -- will only serve to drag out the proceedings. Plus, many say there's little appetite for such a time-consuming fight, given that legal battles may ultimately not be successful and could force the courts to rule on hugely consequential constitutional issues about the separation of powers between the branches of government.

McConnell has little margin for error since it would take just four Republican defections to join with 47 Democrats in order to issue a subpoena. But his increased warnings that subpoenas could prompt an "indefinite" delay in the trial and get tied up in the courts have been gaining traction within his conference, GOP senators and aides told CNN.

Alaska Sen. Lisa Murkowski, a key GOP swing vote, says she's undecided about backing a subpoena for key witness testimony or to force the White House to produce documents. But when asked Thursday if she had concerns about an executive privilege fight tying up the impeachment trial, Murkowski questioned the House Democrats' decision to skip the courts because they wanted to avoid a drawn-out legal battle.

"The House made a decision that they didn't want to slow things down by having to go through the courts," Murkowski told CNN. "And yet now they're basically saying you guys gotta go through the courts. We didn't, but we need you to."

Sen. James Lankford, an Oklahoma Republican, said: "There will be parts of their testimony, they will be covered by executive privilege and parts that are not. Those have to be litigated. That'll take a couple of months to be able to go through the process."

Lankford, reiterating concerns voiced by many other Republicans, added: "To ask us to take a trial that can be two to five weeks and stretch it out to two to five months because they didn't already do this? We can answer the question that they're asking us right now without having to go through all that.'

Democrats have said that the four witnesses -- who have been blocked by the White House -- and four sets of documents would shed crucial light detailing Trump's role in leveraging the power of his office to push Ukraine to announce investigations that could help him politically.

Witness fight leads to legal battle

Republicans are far from sold.

Behind closed doors, Republican senators have discussed for weeks the implications of subpoenas for witnesses, including at a closed-door lunch Wednesday with former Bush attorney general Michael Mukasey.

Many have thrown cold water on any deal that would include a potential trade to secure witnesses whom the GOP wants, including Joe Biden's son Hunter Biden, in exchange for ones demanded by the Democrats. The reason: The White House won't let the Democrats' witnesses testify without a court fight.

"I think it's fair to say there's quite a bit of discussion about just the nuts and bolts. ... Let's say that the House managers asked for Bolton, and the Senate should subpoena him. What would happen next?" said Sen. Josh Hawley, a freshman Republican from Missouri. "If the White House chose to seek an injunction or to test that in court, which is certainly their right to do, that would inevitably stretch things out, we don't know how long."

The senior Missouri senator, Roy Blunt, a member of GOP leadership, said the GOP is weighing if "the witness would change the result."

"Not would the witness tell us something we might not know because we just like to know?" Blunt said. "But would the witness change the result -- and is it worth continuing to reward the bad performance of the House to stretch this out and for not a change in the outcome?

Under the Senate resolution governing the impeachment trial, the Senate will have four hours of debate on a motion about whether subpoenas for witnesses and documents are in order -- once the House impeachment managers and Trump's defense team make their opening arguments and after senators ask up to 16 hours of questions.

After that four-hour debate, the Senate will vote on whether it should consider any motion to subpoena witnesses or documents. If there are 51 votes for that measure, a subpoena would be issued only if the Senate were to approve another motion naming the individual or documents that is backed by a majority of senators. Any witnesses would first be deposed privately before the Senate would vote on whether to make their testimony public.

In addition to Murkowski, the focus has been on Republican Sens. Mitt Romney of Utah and Susan Collins of Maine, both of whom have signaled a willingness to hear from witnesses. Sen. Lamar Alexander, a retiring Tennessee Republican who is an institutionalist and a close McConnell ally, has not ruled out subpoenas either.

But a GOP source close to the group of swing senators argues that the possibility of a drawn-out court fight will weigh heavily, including on Alexander.

On Thursday, Alexander indicated he had not yet made up his mind about supporting subpoenas for witnesses and documents.

"We are doing a really good job of allowing the House managers to make the case. ... They say themselves they presented overwhelming evidence, they've done a good job of that. And then we can decide if we need additional documents or evidence."

Asked if additional documents could help his decision making process, "There's no way to tell that. I think we are doing it in exactly the right order. ... First we are hearing the case .. and then if we need more evidence, we have a right to vote for it. I'll make a decision when we get to that point."

Yet even though Democrats are close to winning 51 votes to issue a subpoena, the expectation on Capitol Hill is that there would need to be more than 51 to be successful, since no GOP senator would want to be seen as casting the decisive vote. That means Democrats would likely need to win over five or more defectors, a tall order in the polarized climate during the high-stakes trial.

Aligning with the President

Most vulnerable Republicans up for reelection this year are quick to side with Trump.

Sen. Thom Tillis, an endangered Republican from North Carolina, has allied himself with Trump in the run-up to his reelection bid this year. On Thursday, he indicated he's ready to acquit the President and said he has no concerns about Trump's conduct, despite the detailed case laid out by House Intelligence Chairman Adam Schiff of California and his fellow Democratic impeachment managers

"No," Tillis said when asked if he had any concerns with Trump's conduct. "What concerns me is Mr. Schiff is spending most of his time saying, 'Boy, I wish I had more time to make my case.' "

Trump's closest allies on Capitol Hill are urging him to invoke privilege if the Democrats succeed in issuing subpoenas for Mulvaney, Bolton, White House budget official Michael Duffey and Mulvaney's deputy Robert Blair -- all four of whom have been demanded to testify by Senate Minority Leader Chuck Schumer of New York.

Both Sen. Lindsey Graham of South Carolina and Rep. Mark Meadows of North Carolina said they'd urge Trump to invoke executive privilege if Bolton were called -- and several Republicans expected Trump to take that tack for any of the four witnesses the Democrats want.

"Executive privilege is a very important separation of powers issue here, and I don't want to see the presidency weakened," Wisconsin Sen. Ron Johnson told CNN on Thursday. "Do we want to stretch that thing out for months? You know, going through legal process because the President will, and should, challenge those types of subpoenas."