Both Collins and Murkowski said Monday they did not plan to co-sponsor the Graham-McConnell resolution.

“I have been critical of the House not holding a vote to authorize the inquiry, but the House determines its own procedures,” Collins said, who has not decided whether or not she would vote for the resolution if it came to the floor. “Just as I don’t like it when House members try to tell us to abolish the filibuster, I’m not sure it’s productive for the Senate to try to dictate to the House how to conduct the inquiry.”

Murkowski, in a statement, also criticized Pelosi and House Democrats for handling the “impeachment inquiry poorly” and for a “serious lack of transparency.” But she added that “as awful as their process is, the formal impeachment inquiry lies in the House, and it’s not the Senate’s role to dictate to the House how to determine their own rules.”

Romney said in an interview Monday that he would look at the resolution but noted that may no longer be necessary.