It's an idea loaded with skepticism, but some Democrats -- desperate for any kind of action on the issue -- consider the President a possible wild card in swaying Republicans who have opposed gun control measures.
"He's the key to unlocking anything that could happen on gun control," said a senior Democratic aide. "If Republicans are going to move, it's because he makes them."
Sen. Joe Manchin, D-West Virginia, said that the partisan climate in Washington has only grown worse since Congress last tried and failed to pass an expanded background check proposal, a bipartisan bill he authored with Republican Sen. Pat Toomey in 2013.
Still, Manchin argued that the measure might have a better chance now under the Trump administration, saying gun owners will trust Trump more than they trusted President Barack Obama with their firearms.
"In the atmosphere we have in Washington, President Trump would set the agenda and set the tone if it's ever going to change or happen," Manchin said.
The White House, however, has shown no movement in the Democrats' direction. Top administration officials are urging surrogates to push back on the idea of pursuing new gun control measures, according to a GOP source in touch with the White House on messaging.
"Let's gather the facts before we make sweeping policy arguments for curtailing the Second Amendment. The investigation is still in its earliest stages," one White House talking point said.
On Tuesday night, Trump appeared to shut the door on gun control -- at least at that very moment. When asked by reporters aboard Air Force One about whether he was open to a discussion on gun control, the President said, "at some point perhaps that will come. That's not today."
'We are stuck'
Following the deadly massacre in Las Vegas that left 59 dead and more than 500 wounded, Democrats have sought to bring the gun control debate back to the limelight, while Republicans have remained largely quiet.
House Speaker Paul Ryan told reporters Tuesday he wants to let the dust settle from Las Vegas before moving on to a legislative debate and pointed to a mental health bill that Congress passed last year.
For his part, Trump also told reporters Tuesday morning that "we'll be talking about gun laws as time goes by."
Democrats, who acknowledge they have little power being in the minority, are fuming. "We are stuck," said Rep. Linda Sanchez, D-California.
While some have taken to less than senatorial language to express their frustration -- "It's time for Congress to get off its ass and do something," Sen. Chris Murphy said in a statement -- others have taken to sarcasm
"Republicans have shown how concerned they are about this; they lowered the flags over the Capitol," said Sen. Patrick Leahy, D-Vermont. "My, that's going to help keep us safe."
Democrats consider alternative route
Frustrated with their Republican colleagues in Congress, Senate Democrats turned their attention Tuesday toward the President and discussed some of his past rhetoric on gun control during their weekly closed-door policy lunch.
While Trump's rhetoric was fiercely pro-Second Amendment on the campaign trail, and while his sons are known as avid hunters, some senators emerged from the meeting pointing to mixed signals he's given on gun control in the past.
In December 2012, Trump praised then-President Obama for his speech in Newtown, Connecticut, after the Sandy Hook Elementary School shooting. In that speech, Obama pledged to work toward change to combat gun violence, saying society wasn't doing enough and signaled he would push for both gun control measures and mental health laws.
While Trump wasn't specific about what he liked in Obama's speech, he tweeted
that "President Obama spoke for me and every American in his remarks."
Asked by someone on Twitter in 2013 for his take on gun control, Trump responded
, "Big Second Amendment believer but background checks to weed out the sicko's are fine."
In his presidential campaign, however, Trump offered a different view, saying in a policy paper that "gun and magazine bans are a total failure."
Though Democrats are doubtful that Trump will side with them on the issue, they're not ruling him out -- or at least a messaging strategy to put the ball in his court.
"If he is true to what he has said earlier, he could be a huge ally," said Sen. Tim Kaine, D-Virginia.
"That he once favored it gives me hope that maybe somewhere down the line he'd be in favor of that again," said Sen. Tom Carper, D-Delaware.
"I'm not optimistic, but I never give up hope," said Sen. Ed Markey, D-Massachusetts.
Asked at a news conference if Trump was the only factor that could end the gun standoff, Senate Minority Leader Chuck Schumer said he's "the most logical" choice. And for the second time on Tuesday, Schumer ramped up pressure on the President, partly using a page out of Trump's own playbook: flattery.
"It's really his responsibility to do this. In the past, he's been very reasonable about the gun issue," Schumer said.
But then Trump ran for president and "had to do what the NRA wanted him to do," Schumer added. "Now, it would be an act of courage, strength, and popularity to do something."
Over on the House side, Rep. Mike Thompson, D-California, chairs a gun violence prevention task force and said Tuesday they were drafting a letter to the President, asking him to support their push to hold hearings and a vote on a background check bill.
"We ask him to join us and try and figure out a solution to help prevent gun violence," Thompson said. "That letter will go out today."