Jeb Bush once handed Hillary Rodham Clinton an award for “public service.” Does this disqualify him from the 2016 Republican presidential race?

At least one influential conservative group thinks it does. ForAmerica, an organization founded by the veteran Washington rightward figure L. Brent Bozell, released an ad-like video Wednesday attacking Mr. Bush as “unelectable” due to his presence onstage with the likely Democratic nominee at a Philadelphia ceremony about 18 months ago.

“It’s bad enough that Hillary Clinton will likely use footage from this event against any Republican nominee, but if Jeb Bush is her opponent she will make him look ridiculous,” Mr. Bozell said in a statement.

Here’s the background: Bush is chairman of the board of trustees of the National Constitution Center, a Philadelphia organization chartered by Congress to “disseminate information about the United States Constitution on a non-partisan basis.”

His brother W. is listed as a “chair emeritus.” So is one William F. Clinton. Ex-presidents tend to flock together, you know.

Back in September 2013, the Constitution Center awarded Mrs. Clinton its Liberty Medal for her international work and efforts on behalf of women and children. At the time she was a few months retired from her post as President Obama’s secretary of State.

The ForAmerica ad juxtaposes this event with Benghazi. Its ad opens with a reminder that the ceremony took place about one year after four Americans were killed in Benghazi, Libya, including US Ambassador Christopher Stevens.

Then it cuts to a clip of Bush on-stage at the National Constitution Center.

“I want to say ‘thank you’ to both Secretary Clinton and President Clinton. Thank you for your service to our country. We are united by a love of country and public service,” says Bush.

The video then says that Clinton denied requests for extra security in Benghazi, and that the attacks occurred on her watch. It cuts to a clip of her giving Jeb Bush “a special thank you.”

It ends with the words, “Hillary will use this event to blunt any criticism that Bush levels against her. Jeb Bush: Unelectable.”

Is this really that bad for Bush? We don’t see it. His words on their face are anodyne. Thanking one’s political opponent for their public service is a basic level of civility, to most voters.

The Benghazi connection might get a bit more of a response. But even there, the response is unlikely to be enough to electorally matter. As the right-leaning Allahpundit says at Hot Air, at the moment Benghazi is the moral equivalent of Obama’s “You didn’t build that” gaffe of a statement in 2012, “something that gets the right excited but which most voters, while ‘concerned’ about it, just aren’t going to care much about when they’re in the booth.”

That said, what this attack ad really shows is that Bush still has a real problem to his right. Yes, he’s a GOP front-runner. Yes, he’s worked hard to earn nods from famous Republican figures (We’re looking at you, Henry Kissinger.)

But conservatives are suspicious that Bush is squishy on immigration and likes Common Core educational standards a bit too much. An interesting new CBS News poll has a cross tab that points this out. Among respondents who rate themselves “very conservative,” 39 percent said they could consider backing Bush for president, but 37 percent said they would not. Wisconsin Gov. Scott Walker does much better with this group, as 50 percent said they’d consider voting for him.

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One way Bush might improve on his standing with the party’s right wing is to emphasize his record as Florida governor, according to a Wall Street Journal piece Thursday. He pushed through $19 billion in tax cuts, and vetoed $2 billion in pork-barrel projects for local legislators while expanding Florida’s gubernatorial powers.

“As the two-term Republican governor of Florida, Mr. Bush was one of the country’s most vaunted conservative champions,” writes Beth Reinhard of the WSJ.