Americans for Responsible Solutions is also planning campaigns again other senators — including four Democrats — who last week helped defeat the background checks bill negotiated by Sens. Pat Toomey (R-Pa.) and Joe ManchinJoseph (Joe) ManchinThe Hill's Morning Report — Sponsored by PhRMA — Trump caves under immense pressure — what now? Election Countdown: Family separation policy may haunt GOP in November | Why Republican candidates are bracing for surprises | House Dems rake in record May haul | 'Dumpster fire' ad goes viral Manchin up 9 points over GOP challenger in W.Va. Senate race MORE (D-W.Va.)

At the same time, the Giffords group is issuing thank-you messages for some of the senators who voted in favor of the bill.

The Americans for Responsible Solutions ad against Ayotte features two women discussing how it "didn't take long for [Ayotte] to 'go Washington'" and vote against what they say were the wishes of New Hampshire voters. 

"This was common-sense legislation written by a Republican and a Democrat, supported by law enforcement, and it protected Second Amendment rights. But Ayotte voted against it anyway," one woman says.

"And ignored the will of the people," another woman says in the ad.

It cites polling that indicates 89 percent of respondents in New Hampshire support universal background checks and urges listeners to call Ayotte's office and "tell her to listen to the people for a change."

The ad running against McConnell also urges listeners to call McConnell and invokes the elementary school shooting last December in Newtown, Conn., where 20 children and six adults were killed by a gunman.

"We watched. We listened. We felt it. Newtown. But Sen. McConnell won’t listen to us," a narrator says.

The narrator charges that McConnell put "the Washington special interests ahead of Kentucky … again," citing polling that shows 82 percent of Kentuckians support universal background checks. 

McConnell is unlikely to vote in favor of gun control — regardless of pressure from gun control advocates — as he's up for reelection in a red state next year and faces a potential primary challenge from the right. 

But Ayotte, who will be up for reelection again in 2016 in a state that leans blue, is considered by many a potential vote in favor of expanded gun control legislation in the future.

Recent polling has shown support for new gun control measures declining as Americans move past the Newtown shootings. A new USA Today poll showed support dipping below 50 percent; in February 61 percent supported stricter laws.

The background checks measure failed on a largely party line vote last week. 

It was supported by all but five Democrats, and opposed by all but three Republicans. Senate Majority Leader Harry ReidHarry Mason ReidAmendments fuel resentments within Senate GOP Donald Trump is delivering on his promises and voters are noticing Danny Tarkanian wins Nevada GOP congressional primary MORE (D-Nev.) voted against the bill as a procedural move that would allow him to bring the measure back to the floor at a future date. 

Gun control groups insist that grassroots enthusiasm is on their side. They argue that persistent pushback against pro-gun forces like the National Rifle Association can still shift votes in favor of expanded gun control legislation.

Americans for Responsible Solutions noted that it received contributions in amounts less than $50 from more than 24,000 people online since last week's vote. The contributions are "a sign of extraordinary anger and determination from Americans throughout the country" who want stricter laws, the group said.