A group trying to make gun violence a factor in pivotal Senate races faces the challenge of educating voters on the candidates’ positions.

Americans for Responsible Solutions released polling data Thursday that showed a majority voters in Florida and New Hampshire either  mischaracterized or were unaware of the Republican incumbents’ positions on expanding background checks on firearms purchases.

Sens. Marco Rubio, R-Fla., and Kelly Ayotte, R-N.H., both voted against an amendment in June that would have expanded background checks to firearm sales at gun shows and online.

According to the group’s spokesman, voters in the poll were asked if they thought Rubio or Ayotte “supports or opposes requiring background checks on all gun sales?”

The polling showed that 69 percent of respondents believed Rubio supports background checks on all sales or were not sure of his position. In New Hampshire, 59 percent of respondents believed Ayotte supported expanded background checks or were not sure of her position on the issue.

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The poll, which surveyed more than 900 registered voters in Florida and more than 800 in New Hampshire, also showed tightly contested races in both states. In Florida, 42 percent of respondents backed Rubio compared to 40 percent who backed Rep. Patrick Murphy, D-Fla., with 17 percent undecided. In New Hampshire, 42 percent backed Ayotte, compared to 47 percent who supported Democratic Gov. Maggie Hassan.

A plurality of survey respondents in both states — 48 percent in Florida and 47 percent in New Hampshire — said they were less likely to vote for a candidate who opposes background checks on gun sales.

Former Rep. Gabby Giffords, D-Ariz., and her husband, Capt. Mark Kelly, founded Americans for Responsible Solutions to support officials and candidates who support solutions to gun violence. Giffords was shot in the head in 2011 during a constituent event in Tucson, Ariz.

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The political action committee has named Ayotte one of its top targets during this campaign cycle. The group launched an ad in May titled “Safety” that said Ayotte voted against background checks. 

“She stands with the Washington gun lobby,” the ad’s narrator said.

Ayotte’s campaign responded with an ad titled “Truth,” noting she voted for background checks, citing a vote for an amendment offered by Sen. Charles E. Grassley, R-Iowa.

Grassley’s amendment covered a number of areas, including increasing funding for prosecutions against criminals who obtain firearms, increasing and clarifying mental health records that are fed into the national background check system, and allowing for interstate gun sales.

Al Bracket, Chief of Police in Atkinson, N.H., cited the amendment in the Ayotte ad, saying, “Kelly’s voted for background checks, with more prosecutions and tougher penalties on criminals.”

Americans for Responsible Solutions responded with a second ad in July titled “Mislead” that highlighted Ayotte’s votes against expanding the background check system.

Jeffrey Pollack of the Global Strategy Group, which worked in partnership with Americans for Responsible Solution on new campaign messaging, said ads were key in educating voters on candidates’ positions.

“That information isn’t out there aside from the sort of chattering class that we all talk to regularly. The average voter doesn’t know it,” Pollack told reporters on a Thursday conference call. “So the only way they are going to find out is by advertising. That’s the thing, when you have a number that’s so big like support for background checks, people are consistently amazed that anyone could be against it.”

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The executive director of Americans for Responsible Solutions, Peter Ambler, said the group planned to use its “Vocal Majority” bus tour to educate voters. Ambler said the bus tour would be particularly focused on bringing national leaders to Florida to generate attention around Rubio’s record on gun control.

Though they won’t be using the phrase “gun control.” Along with the polls numbers, the group released a new guide for candidates discussing preventing gun violence on the campaign trail.

Among the tips were to use phrases such commonsense gun laws, reducing gun violence, gun violence prevention, reducing gun tragedies, in lieu of “gun control.” Campaigns were also encouraged to reference the “gun lobby” instead of the National Rifle Association specifically.

“The opposition is not the NRA. The opposition is the gun lobby,” said Pollack. “What the average NRA member isn’t, is a gun lobbyist.”

Campaigns were also encouraged to dispel confusion about current gun laws, discuss solutions, and create urgency around the issue.

Contact Bowman at bridgetbowman@rollcall.com and follow her on Twitter at @bridgetbhc.