That number would give Republicans enough votes to reach a simple majority in the Senate if Vice President Mike Pence cast a tie-breaking vote in favor if it comes to the floor. If Senate Democrats were to filibuster, however, that would raise the threshold needed to 60 votes.
The resolution is critical of the way House Democrats are conducting the impeachment inquiry and calls on the House to hold a vote to initiate a formal inquiry.
It argues that the House is “denying President Trump basic fairness and due process accorded every American.”
That leaves just three Senate Republicans who have not signed on in support of the resolution, according to the list sent out by Graham: Mitt Romney of Utah, Susan Collins of Maine and Lisa Murkowski of Alaska.
Romney’s office, through a spokesperson, said the senator “would take a look at it, and that he’d like to see a vote in the House and a more open process.”
Hannah Ray, a spokeswoman for Murkowski, told CNN, “Senator Murkowski hasn’t yet reviewed the Graham resolution yet. So she will review the resolution before making a determination.”
CNN has reached out to Collins’ office with a request for comment on the resolution but has not received a response.
Murkowski and Collins are known as among the more moderate Senate Republicans.
Collins is up for reelection in a state that Hillary Clinton won in the 2016 presidential election and is a top target of Democrats hoping to flip the seat in an effort to win back the Senate.
This story has been updated with additional developments Friday.