But don't expect Congress to do something big. The party that tends to support looser gun laws controls both chambers, and President Trump has appeared to double down on a pro-gun position to arm some teachers.
Here's what Congress appears to be seriously considering on gun laws, ranked in order of least likely to most likely:
3. Congress might ban “bump stocks”: Since the Las Vegas shooting in October, there's been bipartisan support to ban a device the shooter used that can make a legal semiautomatic weapon fire more like an illegal fully automatic gun.
Why this might not happen: Bump stocks may indeed get banned, but probably not by Congress. This proposal has perhaps the most bipartisan support of all gun-control measures floated recently, including from the president himself. But Republicans in Congress have deferred to the federal agency that approved the device in the first place to act (a decision in line with the National Rifle Association). That brings its own hurdles. It's not clear whether the Bureau of Alcohol, Tobacco, Firearms and Explosives has the legal authority to ban the tools without a law that makes them illegal.
On Monday, Trump suggested he'd override whatever red tape ATF might get stuck on, although it's not clear he'd be able to if doing so could break the existing law. “I'm writing that out myself,” he said. “I don't care if Congress does it or not.”
2. Congress might raise the age from 18 to 21 to buy assault weapons: This policy hasn't really been on the radar of gun-control advocates, who would prefer tightly regulating or banning these kinds of weapons.
But it's jumped onto the priority list of some members of Congress as a kind of compromise because the accused 19-year-old shooter legally bought the assault weapon. Sens. Jeff Flake (R-Ariz.) and Dianne Feinstein (D-Calif.) are working on a bill to raise the legal purchasing age to the equivalent age for alcohol, and it's gotten the nod from some pro-NRA Republicans in Congress and from Florida Gov. Rick Scott (R), who also broke with the NRA.
Why this might not happen: Support from high-profile Republicans such as Scott might not be enough. House Speaker Paul D. Ryan (R-Wis.) has promised House Republicans he wouldn't bring a bill to a vote on the House floor unless it had the support of the majority of those same House Republicans. And unless behind-the-scenes negotiations are changing a lot of minds right now, support seems tilted toward keeping the buying age where it is.
1. Congress might tighten existing background checks: The most recent change to background checks came in 1993, when Congress instituted a federal background-check system. But gun-control advocates say that system leaves much to be desired. It's understaffed and underfunded, and there are ways to get around it by buying a gun at largely unregulated gun shows or online.
Enter a bipartisan bill led by one of the top Senate Republicans, Sen. John Cornyn (R-Tex.), and Democratic Sen. Chris Murphy (Conn.). It wouldn't expand background checks, but it would require federal agencies to report people's criminal records into the federal background-check system in a modest effort to make it more expansive.
Why this is most likely to happen over all other gun-control measures: A version of this already passed the House, although staunch pro-gun lawmakers got something in exchange for it: a proposal that would allow gun owners to carry concealed weapons across state lines.
Nineteen House Republicans are pressing Ryan to vote on this bill again, without the concealed-carry aspect that makes it dead on arrival in the Senate. Trump and the NRA also support this.
What Congress probably won't do on gun control
1. Congress probably won't reinstate a ban on assault weapons: The top demand from gun-control advocates in the Parkland community is to ban the gun used in the attack, a semiautomatic weapon that can fire rounds twice, three times as fast as a handgun.
Congress banned the guns for a decade in 1994, but they let that expire in 2004 as partisanship on guns hardened and in response to inconclusive evidence about whether it reduced mass violence.
Today, even some Republican lawmakers who seem open to modest gun-control measures don't support the ban or even heavy regulation of the guns. Sen. Marco Rubio (R-Fla.) got into a heavy back-and-forth with the parent of a Parkland victim about this.
2. Congress probably won't expand background checks: Gun-control advocates' No. 1 priority is to pass a law requiring any gun purchaser to undergo a comprehensive background check.
Right now, people who buy guns at gun shows and online don't have to go through a background check.
Trump has vaguely said he supports “comprehensive background checks,” but he hasn't elaborated on what that means, suggesting he might not be willing to push hard for it.
It's tough to see how a Republican Congress does this without extraordinary pressure. A Democratic-controlled Congress back in 2010 didn't have the political capital to pass gun laws (some Democrats have since said that was a mistake), and Congress failed to expand background checks in 2013 after the 2012 Newtown, Conn., elementary school shooting. A Quinnipiac University poll found that just 43 percent of Republicans support an assault-weapon ban.
3. Congress probably won't arm teachers: This is a Trump-NRA priority, and pretty much only a Trump-NRA priority. Trump has gone so far as to suggest incentivizing arming teachers, giving those who carry a gun to school bonuses. He's used the exact same language as NRA chief executive Wayne LaPierre on how to “harden” schools.
But hardly anyone in Congress appears to be taking this idea seriously. If the political will isn't there right now to tighten gun laws, it's certainly not there to loosen them after Florida.