This is the week when the American people decide if the extraordinary House sit-in is remembered as the sound of gridlock breaking, or the latest evidence of gridlock calcifying.  

Energized advocates for gun control predict it will prove to be the former. Experience says it will be the latter.  

Congress remains as combatively stalemated as ever on the issue, and the evidence suggests the partisan and campaign cash divides have grown only more polarized.  

Support in the Democratic ranks for some new limits on the spread of firearms has essentially maxed out: Last week, 94 percent of the party’s House members participated in the sit-in, while all its senators in town lined up behind a modest bill. At the same time, almost all the money and political energy against gun control has gone to the nearly as monolithic Republicans.

Swing-district Republicans

If that’s going to change, with some fertile middle ground found this campaign season, it will have been unearthed at the insistence of a so-far subdued chorus of voters — in the three-dozen or so Republican congressional districts that pose any threat to swing the other way in November and in half a dozen of the states where Senate control is in the balance.  

[

Gun Compromise Faces Challenges From Right and Left

]  

Wednesday’s planned “day of action” to generate support for gun control is being staged only in Democratic districts, so it’s not capable of moving the crucial needle of public perception. It’s the voters in GOP districts who have the crucial opening to find their voice right now, with gun violence and congressional dysfunction conjoined in the national conversation just as their lawmakers are coming home for the Fourth of July.  

[

Democrats Plan Dozens of Events Wednesday to Protest Gun Violence

]  

The House is in recess, but the Senate plans only an extra-long holiday weekend. When all the lawmakers return from facing their constituents, on July 7, a much clearer assessment can be made:  

Has public pressure for gun control grown significantly, if at all, since Orlando’s record-breaking semiautomatic mass murder was followed by a 15-hour filibuster in the Senate and the nearly 26-hour occupation of the House floor?  

Or has the old political adage held: that the lopsided majority in favor of more regulation won’t threaten to vote on that one issue while the small minority of Second Amendment purists absolutely will?

Legislative solutions

The genesis for a legislative breakthrough, albeit a very incremental one, is in view. (It would be the first new federal gun control law in 22 years.) Democrats have concluded that “No fly, no buy” is the most salable concept immediately available, and a growing clutch of Republicans is open to embracing the idea so long as several caveats are attached.  

Such a proposal lurched forward on both sides of the Capitol in the hours after the marathon, social-media-live-streamed protest  was brought to a close.  

It would prohibit firearm purchases by about 109,000 people on certain watch lists (only 3 percent of them U.S. citizens) now barred from commercial airline flights or subjected to heightened levels of screening because the FBI has terrorist suspicions. The FBI would also be alerted to gun purchases by anyone on those lists in the previous five years, language that would have applied to Omar Mateen, the Florida mass shooter .  

Those named in the government’s much bigger terror screening database could still buy guns. And those alleging they were wrongly on the lists would have an expedited appeals process and would get their legal fees reimbursed if they prevailed.  

A symbolically important majority of 52 senators supported that package in a test vote Thursday : All 44 from the Democratic caucus who were in town plus eight Republicans, three in highly competitive races for re-election: Kelly Ayotte of New Hampshire, Patrick J. Toomey of Pennsylvania and Mark S. Kirk of Illinois.

Three other GOP incumbents in close contests — Rob Portman of Ohio, Richard M. Burr of North Carolina and Roy Blunt of Missouri – have each taken $4,950 checks in this campaign from the National Rifle Association’s political action committee. (The chief argument against the proposal is that the watch lists are too flawed to be used as a tool for gun regulation.)

Getting GOP support

In the House, however, the same proposal was introduced Friday by a bipartisan group spearheaded by two of the Republicans most vulnerable to defeat in November — Carlos Curbelo in South Florida and Robert J. Dold in suburban Chicago. (Dold was the biggest 2014 beneficiary of independent spending by the Independence USA PAC , one of the groups Michael Bloomberg created to boost support for gun control.)  

Another such organization started by New York’s billionaire former mayor, Everytown for Gun Safety , was planning to dispatch volunteers this week to attend town hall meetings of Republicans they view as persuadable to back the new bill — including two senators seeking re-election, Florida’s Marco Rubio and Wisconsin’s Ron Johnson.  

If the GOP rank-and-file returns next week to describe a palpable increase of intensity in support of gun safety legislation, Speaker Paul D. Ryan of Wisconsin could be persuaded that it’s in his and the party’s election-year interest to reverse course and allow a straightforward vote on the “No fly, no buy” bill — even though that would mean acceding to the demands of the same Democrats he derided for staging a “publicity stunt” and who then confronted him on the House floor with boos and shouts of “Shame!”

To be assured of moving through the House, the measure would need support from more than three-dozen Republicans, who would join almost all the Democrats.    

Of the 11 House Democrats (out of 187) who stayed away from the chamber during the sit-in, seven have received NRA donations in this decade. The same can be said for only four of the protest participants.  

That’s illustrative of how the political money on both sides has been flowing in ever-more partisan patterns. Six years ago, the last time a critical mass of culturally conservative Democrats helped that party hold the House majority, the NRA donated $350,000 to 65 of the party’s candidates. Those numbers both got cut in half in 2012, and in the past election, just 13 Democratic candidates shared $38,000.  

So far this cycle, the NRA has written just two checks to Democrats, totaling $3,500 — precisely 1 percent of what the NRA has already donated to Republican congressional candidates.  

“We are stepping into a new world in terms of this struggle. Of a widening universe of advocates, of a widening circle of different sectors of demographics in our country,” House Minority Leader Nancy Pelosi said in assessing the politics of gun control after the protest ended.  

If that’s to prove true, and for the Republicans to realize it as much as Democrats, then more demonstrable evidence in political money and constituent sentiment will need to surface soon.  

Get breaking news alerts and more from Roll Call on your iPhone or your Android.