Sen. Mark Pryor, the embattled Democratic incumbent in Arkansas, made a serious gaffe in March when he questioned Republican opponent Tom Cotton’s reliance on military service as a campaign theme.

While praising the congressman for serving, Pryor told a TV interviewer that he didn’t consider Cotton’s military record in Iraq and Afghanistan a special credential. “I think that’s part of that sense of entitlement that he gives off,” Pryor said. “Almost it’s like, ‘I served my country, let me into the Senate.’ ”

For Cotton, who turns 37 on Tuesday, it was a gimme: He filmed a playful ad with his Army drill sergeant responding to the “entitlement” charge. “Did I say ‘At ease,’ Cotton?” the sergeant barks.

The ad went viral. But, surprisingly, it seems not to have helped Cotton’s campaign.

A New York Times Upshot/Kaiser Family Foundation poll last month before the ad was released showed Pryor with a 10-point lead over Cotton. A NBC News-Marist poll, released Monday, shows Pryor with an 11-point lead. A Pryor win is by no means certain, but the fact that the Democrat is even in contention in a state where President Obama’s approval rating is just 33 percent suggests Cotton’s military record is no magic bullet.

In a series of ads done by and for Cotton, the former Army Ranger’s military career is the centerpiece of his Senate candidacy — and yet that doesn’t seem to be helping him, even though his opponent may be the most vulnerable Senate Democrat in the country.

It’s not just Arkansas: America loves its 2.8 million “heroes” who served in uniform since 9/11, but only 17 veterans of Iraq or Afghanistan are in Congress, according to Iraq and Afghanistan Veterans of America. That includes John Walsh, a Montana Democrat who was appointed to his Senate seat and will have difficulty winning election in the fall.

Of the 17 (14 Republicans and three Democrats), few have campaigned primarily on their service. “These are just not issues that are dominating in the polls right now, on either side,” said Jon Soltz, the head of VoteVets, which promotes the election of progressive veterans.

In 2006 and 2008, Democrats had some success running anti-war vets such as Patrick Murphy, Chris Carney and Joe Sestak, but they later lost races. And, of the Republicans elected, many have been guardsmen and reservists who had held or run for lower offices before; they tend to have strong political connections and aren’t campaigning primarily on their war records.

Military service has never been a guarantee of electoral success, of course. Bill Clinton, who didn’t serve, defeated two celebrated combat veterans. George W. Bush beat two opponents who, unlike him, had served in Vietnam.

But now the wars that dominated the national dialogue for a decade have faded in relevance. A Gallup poll in February found that 49 percent of Americans thought U.S. involvement in Afghanistan was a mistake (48 percent said it was not). A majority of Americans long ago decided that the war in Iraq was a mistake. Also, a Pew poll last year found isolationist sentiment running at a 50-year high, with Americans, by 52 percent to 38 percent, saying the United States should “mind its own business internationally.”

Cotton, a product of Harvard and its Law School, used his military service to distinguish himself in 2012 and win a GOP House primary. He followed the same script this time — but support for his military-themed campaign seems to have hit a ceiling.

In November, he released an ad showing photos of him in Army fatigues posing with military hardware while his mother gave the voice-over: “After Harvard, he gave up a great career to volunteer for the Army. They offered to make him a military lawyer but Tom insisted on the infantry.”

Last month, there was the drill sergeant ad. Now, a group called the Government Integrity Fund is blanketing Arkansas with more martial imagery and photos of Cotton in camouflage. “A tour in Baghdad, another north of Tora Bora,” says one. “For his combat service, Cotton was awarded the Bronze Star. Now, Tom Cotton is ready to serve his country again, to fight Obamacare, bailouts and runaway spending.”

Cotton keeps up the theme, going to the House floor last week to discuss a “couple of lessons I learned in the Army,” including the admonition to “move to the sound of gunfire.”

But Arkansans, it appears, are already well aware of Cotton’s Army career. Now they want to know what he has done as a civilian.

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