"We've heard it claimed that the same House Democrats who botched their own process should get to reach over here into the Senate and dictate our process," McConnell said from the Senate floor. "Let me clarify Senate rules and Senate history for those who may be confused," McConnell added. "First, about this fantasy that the Speaker of the House will get to hand-design the trial proceedings in the Senate, that's obviously a non-starter."

Pelosi has held the two articles, saying she wants details about what the Senate trial would look like. Some House Democrats have argued that if they can't get a deal on "fair" rules, including on witnesses and documents, that the articles should never be sent to the GOP-controlled Senate.

Schumer and McConnell are currently at loggerheads over the process for the impeachment trial. The two traded barbs during back-to-back floor speeches from the Senate floor on Friday, underscoring that the two-week break did little to shift the battle lines in the standoff.

Schumer wants one resolution at the outset of the trial that would tackle both the rules of the proceeding and an agreement on specific witnesses. He knocked McConnell on Friday for using "feeble talking points" and "finger-pointing and name-calling" instead of explaining why the Senate shouldn't call witnesses.

"The Republican leader hasn't given one good reason why there shouldn't be relevant witnesses or relevant documents. We did not hear one from Leader McConnell today or any day," Schumer added.

"Since Congress recessed for the holidays, there have been several, several events that have significantly bolstered my argument for four specific witnesses and specific categories of documents," Schumer said.

But McConnell appeared unmoved on Friday, saying he wants two resolutions, similar to the 1999 Clinton trial. The first would lay out the rules for the proceeding, while the second would determine which, if any, witnesses are called to testify.

"The structure for this impeachment trial should track with the structure of the Clinton trial. We have a precedent here. That means two phases," McConnell said.