During his failed bid to capture the Republican presidential nomination, Senator Marco Rubio did everything he could to highlight his opposition to universal background checks.

The Florida Republican argued on CBS News last December that expanding background checks to all purchases would put an “incredible burden” on gun sellers and would not have stopped the mass shooting in San Bernardino, California. Those claims align with Rubio’s record: He opposed bids to strengthen background check laws in 2013, 2015, and 2016.

But most Floridians didn’t get the message. Nearly 70 percent of registered voters in the state believe that Rubio supports background checks for all gun sales, or are not sure of his view, according to a survey last month by Public Policy Polling on behalf of Americans for Responsible Solutions, the gun safety group founded by former congresswoman Gabby Giffords.

The findings highlight an almost paradoxical challenge with popular gun safety measures. Advocates push proposals like background checks for gun sales, which top 80 percent support in national polls, because many voters consider them common sense steps. Yet because the measures strike many as intuitive, poorly informed voters assume their representatives agree with their viewpoint.

“Background checks seem so obvious to people,” said Angela Kuefler, senior director at Global Strategy Group, which conducts polls for ARS and Democratic campaigns. Voters often assume their congressional representatives are reasonable and agree with what seems a common sense view.

New Hampshire Senator Kelly Ayotte, a Republican, drew ire of gun safety advocates when she voted against the background check bill in 2013. Giffords’ group since May has blanketed New Hampshire with ads faulting Ayotte for her votes on guns.

Polling commissioned by the group in New Hampshire showed that prior to the advertising, 75 percent of Granite State voters believed Ayotte supported universal background checks or were not sure. The ads have changed this impression — at least a bit. By August, 59 percent of voters in the state were incorrect about or unsure of Ayotte’s position.

Public understanding of how their representatives voted on a Democratic proposal to bar people on a federal terror watch lists from buying guns is also skewed. Senate Democrats forced votes on the so-called terror gap bill twice: once after the San Bernardino shooting last December, and again after the deadliest mass shooting ever occurred at an Orlando nightclub in June. Both incidents were carried out by shooters claiming allegiance to ISIS.

Rubio voted against both measures, and against a compromise bipartisan proposal based on a smaller list of terror suspects. Yet 76 percent of Florida voters believe Rubio “supports prohibiting individuals on the FBI Terror Watch List from buying guns” — or said they were unsure of his position.

Lawmakers often use procedural moves to muddy the waters when their legislative votes don’t line up with public opinion. Senate Republicans were reluctant to support the Democratic proposal to close the terror gap, so they offered up an alternative that would have allowed the Justice Department to block gun sales to terror suspects — but only if government officials appeared in court to show probable cause. The bill was faulted by many policy experts for posing too high of a burden on law enforcement officials. But it allowed its Republican backers to argue that they did, in fact, support closing loopholes that allow terror suspects to buy firearms.

On Thursday, Rubio introduced a similar proposal: It requires the Justice Department to show probable cause in court to temporarily block a gun sale to a terror suspect. The measure is unlikely to come up for vote this year.

Republicans have used the same tactic on background check legislation, repeatedly offering an alternative that would not have expanded background laws, but instead pushed for increased prosecution of people who break them. In a May campaign ad, Ayotte claimed that her support for that bill meant she voted “for background checks.”

It’s not just gun laws. Americans are poorly informed about government basics, let alone specific lawmaker votes. A study released Wednesday by the University of Pennsylvania’s Annenberg Public Policy Center found 35 percent of respondents could not name a single branch of the federal government.

Voters are also confused about the laws themselves. In a survey last year, Yale researchers found 41 of respondents incorrectly believed federal law currently requires universal background checks.

“People don’t keep up with these issues,” said Robert Blendon, a professor who heads an opinion research program at the Harvard School of Public Health analyzing public views on health policy.

Gun safety advocates and Democrats are eager to punish Republicans for their records on guns, and are spending millions of dollars to change public perceptions.

Background checks enjoy better than 80 percent backing in Florida and New Hampshire. Barring terror suspects from buying guns tops 85 percent in both states. A plurality in each state say they would vote against a candidate on the basis of their view on gun laws. But voters cannot punish politicians for positions they don’t understand.

[Photo: Dennis Van Tine/Geisler-Fotopres/AP]