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Senator Joe Manchin of West Virginia hasn't given up on passing an expansion of background checks on gun sales. With polls showing that some senators took a hit for opposing the measure, the NRA is working to convince their constituents they did the right thing.

It's a sign that both sides learned a key lesson. After the Senate two weeks ago failed to stop a filibuster of the compromise Manchin worked out with Pennsylvania's Pat Toomey, the president promised that "sooner or later, we're going to get this right." One point Obama made during his speech has come into sharp relief: Politics trump policy. Relying on senators to want to fight gun violence isn't going to cut it. Having them see a political cost just might.

Earlier today, Public Policy Polling, a generally left-leaning polling firm, released data from a series of surveys looking at how voters in some states reacted to their senator's vote on the compromise bill, adding to one it conducted last week in New Hampshire. The PPP data focuses on a decline in approval ratings for the senators — Jeff Flake of Arizona, Mark Begich and Lisa Murkowski of Alaska, Rob Portman of Ohio, Kelly Ayotte of New Hampshire, and Dean Heller of Nevada. That's a tricky measure; lots of things can contribute to a drop in approval ratings.

The more interesting question is buried a little deeper in PPP's results. The firm also asked voters how likely they are to hold the senators accountable for the background check vote at the polls. From that data, it's clear that the vote prompted a negative reaction from those polled. Votes from the six senators to uphold the filibuster, killing the compromise, had a net negative rating from voters at large. (The graph below shows the difference between those saying they were less likely to support the candidate after that vote and those who were more likely.) In every case, Democrats and independents were significantly less likely to vote for the senator. In only four cases did the vote offer a benefit from Republican voters — and even in those cases, the effect was mostly small. In other words: the vote hurt more than it helped, in every case.

There area lot of variables at play here. The margin of error is fairly high, for example. This is only a survey of six senators; others may have seen a different response from their constituencies. Three of those senators (the non-Alaska ones) were the target of ads funded by Michael Bloomberg's Mayors Against Illegal Guns. Flake in particular was hammered in an ad for flipping his position on background checks. That kind of air support may have played a greater role in the strongly negative response.

The NRA is banking on the value of ads to move support. The pro-gun group has launched print and radio ads supporting the anti-background check votes from Montana's Max Baucus (who is no longer running for reelection) and Ayotte. If, as the president argued after the measure's defeat, the struggle for these elected officials is whether or not they will be reelected, both sides are working to ensure that the senators at least think they didn't pay that highest cost for the vote.

Which is the last variable at work in those PPP polls. It's a long time before any of those senators are up for reelection — even Begich, who's up next year. The extent to which background check proponents prioritize this vote over everything else the senators have done is a big question mark. Once every six years, voters offer a real assessment of their senators' job performance. How long their memories are is an important question. Manchin may be best served forcing another vote before everyone forgets.

Photo: A woman who lost a loved one in the shooting in Aurora, Colorado, demands an apology from Flake. (AP)

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