(CNN) With momentum comes movement in Washington, and everyone from President Donald Trump to his Democratic opponents thinks something should be done in the wake of two mass shootings over the weekend.

We have watched the sickening repetition of mass murders by gun-wielding young men across the country and in communities of every type. And we have stood by, stunned, as the lives lost in a moment mounted: 58 dead in Las Vegas, 49 dead in Orlando, 26 at Sandy Hook Elementary School and then, last weekend, 31 in Texas and Ohio.

Washington could not summon a collective will to act after the slaughter of children at Sandy Hook Elementary. But just maybe, this time might be different, spurred by the rapid succession of tragedies.

After days of anger and accusations in which Democrats accused Trump of fomenting hate and Senate Majority Leader Mitch McConnell of obstructing progress, there are signs that something is happening in Washington.

CNN will explore what can be done during a town hall in New York at 9 p.m. ET on Wednesday.

McConnell, while not immediately calling lawmakers back to Washington as Democrats demanded , directed Senate Republican committee chairmen to come up with options to address gun violence. It's far short of support for the universal background-checks proposal that passed through the House in February. And McConnell's openness to a "process" is not the commitment to a vote in the Senate that he has the power to promise.

Perhaps his approach turns into a vote on background checks or a national standard for red flag laws. Neither would necessarily have prevented any of the recent shootings.

But doing nothing is no longer acceptable, according to Scott Jennings, a Republican political commentator and CNN analyst who is close to McConnell.

"That's no excuse for people of goodwill to simply throw up their hands in disgust and say there's nothing we can do," he wrote in USA Today. "There likely isn't a law that can A) pass the Congress that would B) stop all mass shootings. But some laws would signal to the American people that we take this problem seriously."

A Quinnipiac poll from March found 73% of registered voters thought "more needs to be done to address gun violence" in the United States, including majorities across parties (95% of Democrats, 74% of independents and 52% of Republicans). That poll also found 86% in support of the background check bill passed by the House, described as requiring "background checks on all gun sales, including those at gun shows and through online retailers."

Multiple Senate Republicans have expressed their interest in a bill to revamp the background check system like the one that passed the House with bipartisan support.

If there is movement toward a new measure in the Senate, one key question is whether the Democrats who now control the House will accept something less than what they've already passed.

Trump, who has defended himself against accusations that his political rhetoric helps stoke anger and hate, may get an earful from local and state officials when he visits El Paso and Dayton. Neither city's mayor suggested they were particularly excited about his plans, and Democratic Dayton Mayor Nan Whaley said she wanted to hear more from the President about guns.

He tweeted openness to a background checks proposal but did not mention it in prepared remarks he delivered from the White House on Monday.

One argument in favor of the background check proposal is that there is overwhelming support for it from the public at large.

It is notoriously hard to read the public's mind on gun control measures and there is often an increase in support for stricter gun laws immediately after mass shootings.

9 in 10 want better background checks

On background checks in particular, where it seems like the ground is moving most, there is extremely wide public support.

The most recent polling on gun laws comes from a mid-July NPR/PBS NewsHour/Marist poll, which found 89% considered it a good idea to implement "background checks for gun purchases at gun shows or other private sales," with a nearly nonexistent partisan divide: 96% of Democrats, 89% of independents and 84% of Republicans called it a good idea.

One of the authors of the background check bill that nearly passed the Senate in 2013 said he is trying to revive that effort. Sen. Pat Toomey, a Pennsylvania Republican, said he and Sen. Joe Manchin, a West Virginia Democrat, have spoken with Trump about it. He said he thinks there would be more support among Republican senators for the proposal now.

"Maybe it's just the accumulation of pain from all of these horrific experiences," he said Tuesday on CNN. His proposal, which revamps the background check system for commercial gun sales, does not go as far as the House-passed proposal, which requires background checks for private sales too

Toomey, while pushing a better background check system, said on Fox News that he would oppose any type of restriction on sales of so-called assault weapons.

"Guns that are described as assault weapons are almost invariably no more powerful than ordinary hunting rifles," he said, adding, "They're extremely popular, and so to ban an extremely popular firearm, I'm not gonna support that. That would be an infringement on the rights of law-abiding citizens."

Less support for an assault weapons ban

There is less broad support for other measures that Democrats in particular support.

In that NPR/PBS poll, 57% said "a ban on the sale of semi-automatic assault guns, such as the AK-47 or the AR-15," is a good idea; 41% thought that was a bad idea. There was a massive partisan divide here: 83% of Democrats called it a good idea, while only 29% of Republicans agreed. Among independents, 55% said good idea, 43% bad idea.

There is a gender gap on this question that crosses party lines: 71% of women called this a good idea vs. 42% of men. The gender gap holds among partisans, with female Democrats and Republicans more apt than their male counterparts to say it's a good idea (36% among GOP women vs. 23% among GOP men and 87% among Democratic women vs. 76% among Democratic men), but the gap is particularly stark among political independents (78% of independent women backed it vs. 34% of independent men).

More generally, a Quinnipiac University poll in May found that 61% of registered voters supported "stricter gun laws in the United States," while 34% opposed that. Among Republicans, 62% said they opposed it, while a huge majority of Democrats (91%) and most independents (59%) supported it. Among gun owners, support for stricter gun laws stood at 39%, with 56% opposed.

The poll found majorities in favor of "requiring individuals to obtain a license before being able to purchase a gun" (77% supported that, including 92% of Democrats, 75% of independents and 65% of Republicans) and "a nationwide ban on the sale of assault weapons" (63% overall backed that, with a large partisan gap -- 87% of Democrats, 63% of independents and 39% of Republicans supported it).

Texas and Ohio less receptive to gun laws

But the issue also changes from state to state, and that is an important point when considering whether a lawmaker will support a measure. Before the shooting in Dayton, for instance, Ohioans were pretty evenly split. A July Quinnipiac University poll in Ohio found a close division there among registered voters on stricter gun laws in the state, with 48% saying they supported them and 46% opposed.

Similarly, a University of Texas/Texas Tribune poll in February found that 49% of Texas registered voters thought "gun control laws should be made more strict," 17% thought they should be less strict and 30% thought they ought to be left as they are. The poll also found 72% in support of "allowing courts to require a person determined to be a risk to themselves or others to temporarily surrender guns in their possession"; just 18% said they were opposed to that. Ohio's Gov. Mike DeWine, a Republican, has backed such a proposal in the wake of the shootings over the weekend.

But Americans generally are not very optimistic that any progress can be made on gun policies. At the end of 2018, a CNN poll conducted by SSRS asked Americans whether they were optimistic or pessimistic about the government in Washington making any progress on several issues. On gun policy, 58% said they were pessimistic about the government's ability to make progress on the issue in the next few years. That pessimism was stronger among Democrats (73%) and independents (60%), while most Republicans said they were optimistic about it (52%).