"I think the prospect of calling witnesses, in my view, seems unlikely, as much as some people might like to complete the incomplete record," Sen. Kevin Cramer, R-N.D. told reporters Tuesday. "The premise of the whole impeachment process is so warped that completing a bad record just doesn’t make a whole lot of sense to me."
Cramer said calling in live witnesses would be a "risky" move, considering that any motion senators make on the floor during an impeachment trial would require a simple majority – or 51 votes – which are not guaranteed.
Some Republicans had previously wanted former Vice President Joe Biden and his son Hunter, and the anonymous intelligence community whistleblower, whose complaint launched the House impeachment inquiry, to be called on as witnesses.
Trump himself has also repeatedly called for House Intelligence Committee Chair Adam Schiff to testify as part of the Senate trial.
A White House official told Capitol Hill reporters last week that Trump was calling for live witnesses as part of the impeachment trial, instead of relying on videotaped depositions like the ones entered into evidence during former President Bill Clinton's impeachment trial in 1999.
"There’s people who want to call witnesses, there’s people who don’t want to call witnesses," Sen. Lindsey Graham, R-S.C. said. "I think the trial needs to end as quickly as possible."
Senate Minority Leader Chuck Schumer noted during his weekly presser that nothing is off the table at this point in the process when it comes to hauling in witnesses, including Trump administration officials that Democrats have been eager to hear from.
"I’m not going to get into the specifics, but it should be fair, it should be bipartisan and it should let the facts come out," Schumer said.
GOP Sen. Mike Braun of Indiana warned that calling witnesses could be a "double edged sword" for both Republicans and Democrats.
"I think that would be one of the things that might be discussed in terms of consensus going into it," Braun said. "So I think that's a double edged sword that I have no idea how it will turn out."
However, Braun said he’d follow Trump’s lead on the matter.
"I think I'll largely follow the guidelines of what the president wants to do there in terms of litigating his case now that he gets a chance to do so," Braun said.
The Senate’s No. 2 Republican, John Thune of South Dakota, said the desire to finish the impeachment trial as quickly as possible would likely trump the need to call in witnesses.
He said a "protracted period" with motions to call witnesses, offered by both sides of the aisle, and lots of votes isn't going to be popular for anyone.
"I think there's going to be a desire to wrap this up in at least somewhat of a timely way," Thune said.
Democrats on Tuesday unveiled two articles of impeachment against Trump in a historic step that could lead to a full House vote as early as next week. House Judiciary Committee Chairman Jerry Nadler announced that Democrats were going forward with charges of abuse of power and obstruction of Congress.
Senate Majority Leader Mitch McConnell confirmed on Tuesday that a potential impeachment trial in the Senate will take place right after the New Year, once senators return from a holiday recess, even though the White House is urging the Senate to take up the matter immediately.
McConnell said he anticipates House managers will present their case to the Senate, with the president’s lawyers following suit.
"And at that point, the Senate has two choices: it could go down the path of calling witnesses and basically have another trial, or it could decide," McConnell told reporters Tuesday during his weekly press conference. "And again 51 members could make that decision, that they've heard enough and believe they know what would happen and could move to vote on the two articles of impeachment sent over to us by the House."
He added, "Those are the options. No decisions have been made yet."
On potential witnesses, McConnell again demurred and said the Senate would make a decision once opening arguments have been presented.
He reiterated that it remains his view that the Senate will not remove Trump from office because the votes aren’t there.
Ahead of the press conference, Senate Republicans met over lunch with law professor Jonathan Turley, the sole Republican witness who testified before the House Judiciary Committee last week.
During his testimony, he argued that the facts presented by the House Intelligence Committee didn’t meet the necessary standard for impeachment.
Republican senators today said Turley’s presentation before the caucus was to provide an "assessment" about the current status of the impeachment inquiry.
"It was along those lines," Thune said of Turley’s testimony before the House Judiciary Committee last week. "You know, his kind of, analysis of what's happened so far, and you know what a little bit of an assessment of what he thinks could happen going forward."