Murkowski has called out Democrats for their rushed impeachment schedule, as well.
Riley continued, "I do wish she would stop using Democratic talking points to make the argument that she is making. The fact of the matter here is that the House's job is done and this idea that they should have any say in how the Senate conducts this trial just is not supported by what is written in black-and-white in the Constitution."
Riley pointed to the fact that no House Republicans voted with Democrats to impeach Trump, not even retiring lawmakers such as Reps. Will Hurd, R-Texas, and James Sensenbrenner, R-Wis., who he said had "nothing to lose" if they broke with their party.
"The idea that Mitch McConnell isn't going to be bipartisan enough or objective enough, that is not his job. I expect him to be as bipartisan as Nancy Pelosi was and as Adam Schiff and Jerry Nadler were," he added, referring to the speaker and the two committee chairmen who presided over impeachment hearings in a manner widely criticized on the right.
"For me to prejudge and say there's nothing there or on the other hand, he should be impeached yesterday, that's wrong, in my view, that's wrong," she said. "If it means that I am viewed as one who looks openly and critically at every issue in front of me, rather than acting as a rubber stamp for my party or my president, I'm totally good with that."