(CNN) As the impeachment inquiry of President Donald Trump barrels through the House on target to potentially finish by Christmas, senators from both parties are reckoning with their own role and are beginning to discuss if they can agree on a set of rules for a trial.

If the House of Representatives sends over articles of Impeachment , lawmakers could take a page from former President Bill Clinton's trial and pass a resolution that would set forth the rules and procedures. But, it requires broad agreement and without it, senators would default to the already established rules.

During the Clinton impeachment, it took a closed-door meeting and a belief that the Senate had to come before the politics of the moment, to pass a resolution setting the ground rules 100 to 0. Since that time the chamber has taken no shortage of hits, scarred from years of viscerally partisan rifts over policy, nominations and allegiances to presidents.

But as an impeachment investigation -- one that some Republicans have dismissed as a gross attempt to overturn an American election and Democrats have praised as essential to preserving Democracy -- rages on, a key question becomes whether a bipartisan process is even possible in the Senate in the era of Trump.

"That's a great damn question," said Sen. Chris Coons, a Delaware Democrat who recently took to the floor to lay out the stakes -- and place in history -- his colleagues may soon face.

A precedent of bipartisanship

It was January 1999, and there was a growing concern that lawmakers had not agreed to the terms of the Clinton impeachment trial. That is when Vermont Sen. Patrick Leahy, a Democrat, said he went to the Republican and Democratic leaders and urged them to bring lawmakers into the old Senate chamber to hash out the ground rules for the upcoming weeks.

"I went on the floor at about 4 p.m. in the afternoon. (South Dakota Democratic Sen.) Tom Daschle and (Mississippi Republican Sen.) Trent Lott were there -- both good friends, both old school, kept their word that they cared more about the Senate than anything else, and I said 'we still don't know what our procedure will be so why don't we all meet in the Old Senate Chamber, close the doors, keep everybody else out, just talk about it as long as it takes, everybody have a chance to talk and figure out what we want to do,'" Leahy recalled.

Leahy said that the leaders went to the press gallery and announced it.

"We had a couple of members in both parties who were all 'oh you didn't talk to us.' It was irrelevant. We went in there and you had from the most conservative to the most liberal (members), kicking ideas back and forth. And the seriousness of what we were doing, you could feel it settle in ... and we ended up getting procedures," Leahy said.

Over the last several weeks, Leahy said he has tried to convince Senate Majority Leader Mitch McConnell and Senate Minority Leader Chuck Schumer to take the same route again, privately appealing to each of them as well as going to rank-and-file Republican members to make his case.

Democratic Sen. Patrick Leahy of Vermont, speaks during a Senate Judiciary Committee hearing in April 2013 in Washington, DC. (Photo by Mark Wilson/Getty Images)

"Some are so terrified of the White House and that the President might speak against them that they are receptive, but 'Pat don't tell anybody,'" Leahy said.

The next few months will test the Senate and its leaders and force the question of if the body -- with its partisan swings and new, impassioned members -- can separate politics from practicality. A modern-day negotiation comes with added complications. For one, a President who prizes loyalty above all else and may see any Republican concession as a crumbling of his defense.

Senators in both parties profess hope that a bipartisan agreement on the process is still possible.

"It can be," Sen. Roy Blunt, a Missouri Democrat who was in the House during the impeachment of former President Bill Clinton, said when asked if agreement on a similar resolution could be reached. "Hopefully we'll reach that."

Whether that hope can be turned into reality is another question.

"It doesn't do much good to have a process that's fair if it doesn't look fair," Sen. Kevin Cramer, a North Dakota Republican, told CNN. "So I'd be careful to impose rules heavy-handedly on the minority. "

In a chamber where non-binding resolutions of something often get hung up on partisan grounds, the hurdles are many. Close Trump allies are pledging to push for a quick dismissal of any House charges and throwing out the possibility of trying to call Vice President Joe Biden or his son, Hunter, who has been tangled up in unproven allegations tied to the country, as witnesses.

The onus, at least at the start, will fall on McConnell and Schumer to hammer out an agreement. The two have acknowledged they will, at some point soon, need to meet to do just that. That meeting has not occurred yet, aides say.

"I would like to see the Senate fulfill its constitutional responsibilities and do it in a fair, balanced, and orderly way," Sen. Lamar Alexander told CNN. "I suspect most senators feel that way. But we start with the leaders."

One senator present for the Clinton impeachment noted that despite the current state of US political affairs, "when you're in that chamber, silent, with no phone, the gravity of the moment hits you. You just can't ignore it. I suspect that will happen again."

Yet some Republicans, who have already dismissed the House-led process as "a sham" and having already judged Trump innocent before the presentation of evidence, have made clear they are ready to fight the minute the House sends the articles of impeachment across the Capitol.

Sen. Rand Paul, a Republican from Kentucky, has argued he won't support any trial structure that doesn't give the President and his counsel the opportunity to request the whistleblower to be called as a witness.

"I am all in favor of the President calling Joe Biden, Hunter Biden and the whistleblower, and if (House Intelligence Chairman) Adam Schiff thinks he can veto defense witnesses, then it is a complete sham and a farce and I would advise Republicans to not participate in anything that doesn't allow defense witnesses," Paul said.

What happens without an agreement

Senate rules guarantee at least some guardrails. If the House passes articles of impeachment for just the third time in history, it forces the Senate to work six days a week in a trial. Every day, the proceedings would start at the exact same time in the afternoon with senators in their seats with lips sealed. The Constitution isn't clear on what exactly a Senate trial must include, but it does dictate that the Chief Justice, in this case John Roberts, has broad discretion on the scope of the trial.

The rules also dictate that all the senators must take an oath before engaging in the trial and it gives room for the presiding officer to appoint a committee to handle some of the work of the investigation "to receive evidence and take testimony at such times and places as the committee may determine." That is a step many aides and senators have said isn't be considered seriously.

But, if lawmakers can agree to a resolution like the one during the Clinton impeachment, senators can amend the process to their liking and they can potentially preserve the reputation of the Senate as the greatest deliberative body.

"My hope is that we have leaders in both parties who recognize that it's not just the President who would be on trial if impeachment comes to the Senate, but it would be the Senate that is on trial," Coons told CNN.