Senator Jeff Flake of Arizona appears to be reversing his opposition to the background check compromise killed in the Senate last month. It's another sign that the tide is shifting in the gun debate — albeit it on one issue in one chamber of Congress — as advocates continue to apply pressure.

According to CNN, Flake's change of heart centers on provisions related to Internet sales. The original compromise — cobbled together by Joe Manchin of West Virginia and Pat Toomey of Pennsylvania — sought to expand background checks for sales at gun shows and online. Flake wants those latter provisions to be stronger.

Flake said the only reason he voted no was because of his concern that the requirement for background checks on internet sales is too costly and inconvenient, given the way guns are often sold among friends in his state of Arizona and others.

That's the argument he's making anyway. As we've noted, Flake's popularity flattened after the vote. For an elected official to change his mind on a high profile vote in the face of massive public opposition, he has to offer some rationale; it is the job of his colleagues to make that rationale as viable as possible. Maybe Flake always had these concerns. Maybe they came to him in a dream over the last two weeks. Maybe that Aurora mom effectively shamed him. Either way, it's a vote. For a measure that came five votes short of breaking a Republican-led filibuster, it's an important step.

Senate Majority Leader Harry Reid — a former amateur boxer — thinks they're getting close to the other four.

“Joe Manchin called me yesterday. He thinks he has a couple more votes,” Reid said during a brown-bag lunch. He added that Sen. Kelly Ayotte (R-N.H.), the only senator from the Northeast to vote against the measure, has been taking a lot of heat back home for her vote.

“Wham! Man has she been hit hard,” Reid said in the interview. “She went from a hugely positive number in New Hampshire — her negatives now outweigh her positives. She is being hit every place she goes.”

(Most notably when she was confronted by a Newtown mother last week.)

Reid praises the pressure Ayotte faces, but somehow considers similar pressure on Democrats unhelpful. According to Politico, Reid asked Mayor Michael Bloomberg's pro-gun-control group to not run ads in the districts of Democrats that wavered on last month's vote. (He's done this before; in 2011, he criticized the League of Women Voters for its ads attacking Missouri's Claire McCaskill.) Bloomberg's group, Mayors Against Illegal Guns, declined to heed that bit of advice.

It's worth noting that such ads didn't do the trick last time. Nor did the grassroots efforts of Organizing For Action, the offshoot of Obama's 2012 campaign. After strong criticism of its work before the vote, the group released an interactive map showing where it organized actions and the press that resulted. The map looks like this.

It's interesting to compare that with the map of 2012 electoral results, the most prominent success of the same effort.

You can see where the group focused outside of the states where it had carryover infrastructure (like Chicago, where it and the Obama family are based): Arizona, Texas, Colorado, Montana. Organizing for America also pledged this week that it would add more paid organizers, one of the key problems identified in the critique.

The question is whether Mayors Against Illegal Guns or OFA can — or did — make senators fear for their jobs. Former Clinton advisor Paul Begala makes that point in an article for the Daily Beast. The fault for the defeat of the compromise, he writes, "lies with the voters—at least those of us who support common-sense gun safety. Those politicians don’t think they’ll get beaten for voting against gun control." Begala notes the NRA's record in the 1990s of taking out gun control advocates. In Colorado, a group of gun control opponents are hoping to do the same. Recall efforts have been initiated against four Democrats in the state legislature that supported that state's new gun restrictions.

While those politicians are a long way from actually being recalled, the threat is nothing any elected official wants to face. As non-profits, Bloomberg's group and OFA largely can't directly engage in electoral politics. All they can do is work to get voters to understand why senators like Jeff Flake did the wrong thing, and hope it shows up in the polls. In Flake's case, it did.