“My members know the very simple fact that to make a law you have to have a presidential signature,” McConnell told reporters Tuesday.
During a closed-door briefing on Capitol Hill Tuesday, a senior administration official laid out a range of gun control options that Trump is considering, including expanding background checks and a implementing a federal “red flag” law.
“They are working on coming up with a proposal that the president will sign. Until that happens, all of this is theatrics,” McConnell said.
The Senate's top Democrat - Sen. Chuck Schumer of New York - on Tuesday slammed McConnell for calling out Democrats on their "theatrics" and for failing to call up background check legislation that the House passed in February.
"Shame on him. There are people who died. Shame on him. Put the bill on the floor and stop ducking the issue and calling names. Shame on him," Schumer said.
McConnell has said on multiple occasions that he will not put anything on the floor that the president has already vowed to veto.
While Democrats are proposing wide-ranging measures, including universal background checks and federal firearm licensing, some Republicans think their best shot may be to go back to the failed 2013 Manchin-Toomey bill, which would expand background checks on all commercial gun sales.
“The president is interested in doing something in this space," Sen. Pat Toomey, R-Penn., told reporters Tuesday morning. “The idea of having background checks on commercial gun sales makes all the sense in the world and is very broadly supported. I don't think there's any reason to give up yet and I don't intend to.”
Toomey and Sen. Joe Manchin, D-W.Va., co-authored the bill that failed in the Senate following the mass shooting in Newtown, Connecticut, in which dozens of school children were killed.
But some Republicans have criticized the bill for being too far-reaching.
“I would urge all of my colleagues to look at the substance of this legislation. A background check on commercial gun sales does not curb the second amendment rights,” Toomey said.
But he also acknowledged the bill does need work.
“I am not of the view that Manchin-Toomey was handed down to Moses on Mount Sinai. This is open to discussion,” Toomey added.
GOP Sen. Susan Collins of Maine said she thinks Congress will act on gun control – and soon. When asked if she thinks the Senate will pass something in this session, she responded, “Yes, I do.”
“Over the August recess I had extensive conversations with my colleagues on both sides of the aisle, and with the White House, and I'm optimistic that we can reach agreement on a package would pass the Senate,” Collins said.
GOP Sen. Thom Tillis of North Carolina said that he would be willing to consider bills like Manchin-Toomey if he thinks there’s bipartisan agreement.
“I’m open to anything that we can get bipartisan consensus on that also makes sure that we're not overreaching and really beginning to threaten the rights of law abiding citizens of which the majority of people who own guns are,” Tillis said.
Most Republicans admit they can’t get anything done without the president’s buy-in. And they agree with McConnell’s strategy – saying it’s practical to wait and see what the president decides to do.
“It's going to be hard for me to convince Leader McConnell to give up a week or so on the Senate floor for something that is clearly destined to fail,” Toomey said.
“The president has been very thoughtful, he's called me, we've had a number of discussions, he's very interested,” Toomey said. “I think he's learning about this issue and considering he's gotten a lot of ideas thrown at him. So I think he's sorting through this. I'm hoping that the merits of the argument will persuade him.”
“I think it's critically important,” Tillis said of the president’s support. “At the end of the day he has to sign whatever we send to him.”
ABC News' Trish Turner contributed to this report.