When Democratic Senator Mark Pryor of Arkansas voted against a gun background check compromise last month, he was taking a measured political risk. Even as Mayor Michael Bloomberg's anti-gun group announces a plan to spend $350,000 on ads criticizing Pryor, a detailed new poll walks through why it may have made political sense. With another vote on the issue a near-certainty, gun control advocates are fighting to change that calculus.

Conducted by Pew Research, the survey is one of the most comprehensive analyses gun control politics that's come out since the president's renewed focus on the issue. In April, a key component of his effort — a package of policies including background checks, funding for school safety, and increased penalties on trafficking — never received a vote in the Senate after a Republican-led filibuster of a compromise on background checks wasn't ended. That vote was where Pryor bucked his party: he was one of four Democrats to support the filibuster out of principle, helping to ensure that the policy was blocked on a 54 to 46 vote.

The policy, which would expand background checks for gun sales at shows and for private dealers, is one that voters broadly supported at the time — and continue to support. Pew's analysis starts by asking about various policy proposals. Expanded background checks are by far the most popular, regardless of political party.

And not only in the abstract. Voters strongly support the passage of the compromise proposal in particular.

Unlike with background checks on the whole, however, support for the particular Senate bill differs by party — but even Republicans express a majority of support.

If you're curious how closely Americans have been watching the debate, let this serve as a guide. The majority of respondents think it's not at all or not too likely the bill will pass. So far, that's been an astute presumption.

That assessment differs in two demographics. The more educated the respondent, the more cynical he or she is about passage. And each side in the debate — those advocating for gun rights or those supporting more gun controls — is more optimistic about his own chances.

But the two most important points of data in the poll, the two points that show why the background check policy didn't pass in the first place, assess the willingness of each side to advocate and enforce its position.

In the first series of questions, Pew asked what those supporting or opposing new gun control policy had done to ensure their point of view was respected. Both over the course of their lives and during the most recent push for new policy, those supporting gun rights were more politically active on every front polled. They were more likely to have donated to advocacy groups, to have reached out to elected officials, and so on.

And, even more significantly, the group most likely to use a gun vote as a litmus test for political support were conservatives — the group most likely to oppose new control measures.

In these seven graphs, you see the entire debate. Americans want new background checks. They're supportive of the Senate push, though it's become a partisan issue. But they don't think it will happen. That's because it hasn't — because opponents have been far more politically active and Democratic elected officials can safely assume they won't pay a political cost.

Which is why Bloomberg's group is spending hundreds of thousands of dollars. After the April vote, polling showed that those who opposed the compromise paid a political cost. If voters aren't likely to enact punishment at the polls for opposing their preference, advocates of reform feel an urgent need to do what they can to make that punishment tangible now.

Photo: Carol Gaziola talks about the murder of her daughter at a gun control rally in Nevada earlier this week. (AP)