The value of this number, of course, lies in how we assume it applies to the enactment of policy. The more public support for a proposal, in theory, the more likely that proposal is to become law. The ongoing debate over how to respond to mass shooting incidents constantly leverages bits of data like this one as a suggestion for how the American public would like its leaders to proceed.
On guns in particular, though, these numbers haven't effected much change.
In part, that's because there's a gap between questions like this and political practicality. Saying "gun laws should be stricter" is different than saying "I believe that we should ban certain types of weapons." Tightening restrictions for those with mental health problems would make gun laws more strict, and the National Rifle Association has advocated for such policies in the past, but it's not what many gun control advocates really want to see. We repeatedly hear that Americans overwhelmingly support increased background checks, which they do — but it's not clear how that translates into specific policies that Americans would support.
The aftermath of the Sandy Hook shootings continues to be instructive. The measures proposed in the wake of that tragedy included an expansion of background checks at gun shows. That proposal was blocked by a minority of the Senate and never reconsidered — despite the fact that Gallup's poll showed a similar spike in support for stricter laws.
Why? Because gun control advocates didn't have the necessary political leverage to change a few senators' minds. Some red-state Democrats worried about losing their reelection bids in 2014 bailed on the cause. Of the four who voted against the proposal for non-procedural reasons, only one is still in office.
In other words, there are two gaps that aren't shown on the graph above. The first is the 55-44 gap between those who are eager for stricter gun laws and those who aren't (combining the 33 percent supporting the status quo and the 11 percent who want to roll back the laws), which is probably a fairer way of looking at the keep them/weaken them numbers. And the second is between the 55 percent that want stricter gun laws and the percentage of members of Congress who would have to make it happen. That gap is a political one.
It's worth keeping in mind that — even if the Senate weren't in Republican hands and therefore less likely to act — you need 60 votes to pass a new law in that chamber. Even if the Senate reflected America's will precisely, there would still be 44 votes to filibuster.