Schiff declined to say if House managers will use the full 24 hours they are expected to have to make their case, but argued that the schedule proposed by McConnell would set the stage for a "rigged" trial.

"That will be a decision that the House should make, not that the senators should prescribe to go late into the evening. Look there is a wealth of evidence to present here, and we should have the opportunity to present the case as the House chooses to present its case. Not to go late into the evening," Schiff said.

He added that McConnell was opening the door for the trial to go until roughly 1 a.m., if one side used all 12 hours each day, because he hoped "the public will not be watching."

"I think the question is what is ... Sen. McConnell's interest in structuring the trial this way? Is this about hiding the evidence from the American people with late night sessions? Is this about just trying to get it over with?" Schiff added.

The rules resolution is expected to pass the Senate later Tuesday along party lines. A Senate GOP leadership aide defended the decision on process, saying it "provides the same time but more structure for the arguments."

Senate Democrats blasted McConnell on Monday calling the resolution a "cover up" and a "national disgrace."

The resolution also does not admit House impeachment evidence into the trial record until after an initial vote on whether or not witnesses or documents will be in order. That vote isn't expected to take place until after opening arguments and questions from senators.

House impeachment managers released a joint statement on Tuesday saying the proposed process is "rigged."

Schiff added during the press conference that if Republicans support the floated rules resolution it would "prove the Senate guilty of working with the president to obstruct the truth from coming out."

"I do think by structuring the trial this way it furthers our case that what's going on here ... is a cover up," he added.