Top Republican Senator Mitch McConnell laid out rules for the president's impeachment trial on Monday (January 20).
The proposed plan could lead to a speedy trial for Donald Trump.
And it has no guarantee that witnesses or any new evidence would be allowed.
Beginning on Wednesday (January 22) both the House and Trump lawyers would present their arguments.
But they would each be limited to 24 hours to make their case over no more than two working days.
Trump is charged with abusing the powers of his office by pressuring Ukraine to investigate his political rival, Joe Biden and obstructing the House investigation into his conduct.
But - McConnell's plan for the trial doesn't automatically allow the evidence collected by that House probe.
Instead, the Republican-controlled Senate would have to vote later on whether to accept it.
Democrats aren't happy with the plan.
Senate Democrat leader Chuck Schumer called it a national disgrace, and says it doesn't stick to the rules from the 1998 impeachment of Democratic President Bill Clinton.
(SOUNDBITE) (English) SENATE MINORITY LEADER CHUCK SCHUMER (DEMOCRAT-NEW YORK) SAYING: "A trial where there is no evidence, no existing record, and no new evidence, no witnesses, no documents, that isn't a trial at all, it's a cover-up." McConnel's plan for the trial is set to be voted on as early as Tuesday (January 21).
The Senate is highly unlikely to remove Trump from office.
However, the president has sought to diminish the accusations from Democrats as a partisan witch-hunt as he seeks to limit political damage to his bid for re-election this fall.