Senate Judiciary Committee Chairman Lindsey Graham (R-SC) said on Monday that the "Constitutional outrage" by House Speaker Nancy Pelosi (D-CA) "needs to end," and that if it continues into 2020, "the Senate needs to strike back."

Stop playing games with the Constitution.



In our system, you can’t be the Speaker of the House and the Senate Majority Leader at the same time.



The Senate will decide how we dispose of this sham created by the House. — Lindsey Graham (@LindseyGrahamSC) December 23, 2019

"The Senate will decide how we dispose of this sham created by the house," Graham tweeted, referring to the impasse created by Pelosi - who is refusing to transmit two articles of impeachment against President Trump until the Senate agrees to her terms.

If this continues into 2020, the Senate needs to strike back, standing up for our rights and ending this debacle. — Lindsey Graham (@LindseyGrahamSC) December 23, 2019

President Trump also had words for Pelosi on Monday after the Speaker called for "fairness" in a Senate trial.

"Pelosi gives us the most unfair trial in the history of the U.S. Congress, and now she is crying for fairness in the Senate, and breaking all rules while doing so," Trump tweeted, adding "She lost Congress once, she will do it again!"

Pelosi gives us the most unfair trial in the history of the U.S. Congress, and now she is crying for fairness in the Senate, and breaking all rules while doing so. She lost Congress once, she will do it again! — Donald J. Trump (@realDonaldTrump) December 23, 2019

Pelosi says she will only transmit the impeachment articles to the Senate after Senate Majority Leader Mitch McConnell (R-KY) announces the process they will use for Trump's trial.

McConnell has advocated for a similar process to Bill Clinton's 1999 impeachment, which included an initial agreement to first hear the case, followed by a vote on whether to call witnesses.

Speaking with "Fox and Friends" on Monday, McConnell said "we're at an impasse" and "we can't do anything until the speaker sends the papers over, so everybody enjoy the holidays." McConnell blasted Pelosi for trying to "tell us how to run the trial." "Look, what we need to do is to listen to the arguments, have a written questioning period, and then decide whether we need witnesses or not," McConnell said, adding that some Republican senators "have said, 'I am thinking of myself as a juror,'" while others believe "the case against President Trump is very thin." -NBC News

Senate Minority Leader Chuck Schumer (D-NY) has pushed for a single resolution that would outline the parameters for presenting the case, as well as allow for the calling of witnesses such as John Bolton, acting White House chief of staff Mick Mulvaney, and two other advisers.

Republicans, meanwhile, want former Vice President Joe Biden and his son Hunter to testify over alleged corruption, after President Trump asked Ukrainian President Volodomyr Zelensky to investigate several claims.