House Democrats are bringing two charges against Trump over his dealings with Ukraine: that he abused the power of his office by pressing a foreign power to open an investigation into a political rival, and that he obstructed Congress by refusing to comply with the impeachment inquiry.

The House is expected to hold a full vote on the floor as soon as next week. However, McConnell has maintained that the Senate won't proceed to a trial until January, and he has given few hints about what a Senate trial would like.

Pressed during a press conference on Tuesday, the GOP leader declined to say if he thought Trump's legal team or House Democrats should call witnesses, or how they would be handled. Republicans are considering skipping witnesses in an effort to avoid a drawn-out process with politically tough votes.

McConnell reiterated on Tuesday that he did not expect the Senate to reach the two-thirds support necessary to convict Trump. Republicans hold a 53-47 majority in the Senate, meaning that 20 Republicans would have to join Democrats to remove Trump from office.

"I said I would be totally surprised if there were 67 senators who would remove the president. That remains my view. However, we are obligated under the Constitution to turn to it when it comes over, and we will," McConnell said.