Senate Majority Leader Mitch McConnell reportedly is close to finalizing a rule that would allow President Trump's team to move to dismiss the articles of impeachment in the Senate quickly after some evidence has been presented, as a sort of safety valve in case Democrats try to drag out the trial for weeks.

The discussions came as Texas GOP Sen. Ted Cruz told Fox News' "Sunday Morning Futures" that the trial could extend "to six to eight weeks or even longer" if the Senate decided to hear from additional witnesses -- a prospect that could interfere with the imminent presidential primary contests, as Sens. Bernie Sanders, I-Vt., and Elizabeth Warren, D-Mass., likely would get pulled off the campaign trail.

McConnell, R-Ky., wouldn't be obligated to publicize the final version of his resolution setting the parameters of the impeachment trial until Tuesday, but top Republicans have said they supported affording Trump the opportunity to cut the trial short.

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Republican Missouri Sen. Josh Hawley, for example, said he would be "very, very surprised" if McConnell's resolution didn't include that kind of kill switch.

"I am familiar with the resolution as it stood a day or two ago," Hawley told Axios. "My understanding is that the resolution will give the president's team the option to either move to judgment or to move to dismiss at a meaningful time."

Trump, Hawley wrote on Twitter after Axios' article was published, "deserves the right during Senate trial to ask for a verdict or move to dismiss - otherwise trial will become endless circus run by Adam Schiff."

Democrats, meanwhile, have voiced frustration privately that McConnell was holding the final rules for the trial close to the vest.

“The House managers have absolutely no idea what the structure of the trial two days before the trial begins,” one source with House Democrats working on the impeachment trial told Fox News.

The discussion may end up being moot: Law professor Alan Dershowitz, who is set to present an argument against impeachment during the Senate trial, said Sunday it will be clear there will be "no need" for witnesses if his presentation were to succeed. "Criminal-like conduct," Dershowtiz said, was required for impeachment.

For his part, Trump suggested earlier this month that an "outright dismissal" might be appropriate. But, Republicans almost certainly wouldn't be able to muster the votes necessary to end the trial prematurely.

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The issue of witnesses may remain in limbo for a few more days. Alaska GOP Sen. Lisa Murkowski said she's comfortable waiting to decide if more information would be needed as part of the Senate's impeachment trial until after hearing arguments from House managers and attorneys for the president.

Murkowski said Saturday she wanted to make sure there was a process that would allow senators to "really hear the case" and ask questions "before we make that determination as to, what more do we need. I don't know what more we need until I've been given the base case."

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If Democrats were to try adding certain witnesses to an organizing resolution, Murkowski said she expected McConnell would move to table such a request and she would support a tabling motion.

"What I've worked hard to do is make sure that we have a process that will allow for that determination" — whether witnesses or documents would be needed, she said. "But, I want to have that at a point where I know whether or not I'm going to need it."

She said all senators faced political pressures but her responsibility was "not to focus on the politics of where we are but a recognition that we are in the midst of an infrequent and in many ways extraordinary process that the Constitution allows for, and I'm going to take my constitutional obligations very, very seriously."

Regardless of how one viewed the House's handling of the impeachment process, the matter has moved to the Senate, she said, adding later she did not want the proceedings to become a "circus."

No senators were more eager to avoid a circus, and get going with the proceedings, than the presidential candidates facing the prospect of being marooned in the Senate ahead of kickoff nominating votes in Iowa and New Hampshire.

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“I'd rather be here,” Sanders said on New Hampshire Public Radio while campaigning Sunday in Concord.

During the trial, Sanders and other senators are required to sit mutely for perhaps six grueling hours of proceedings daily — except Sundays, per Senate rules — in pursuit of the "impartial justice" they pledged to pursue.

Fox News' Chad Pergram and The Associated Press contributed to this report.