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(Updated 4:15 p.m.) One of Linda McMahon’s campaign ads may have backfired, at least among some of her Republican supporters. McMahon’s staff recently found themselves having to explain on Facebook that the Republican running for U.S. Senate does in fact support a Republican for president.

McMahon is in a tight race with Democratic U.S. Rep. Chris Murphy for retiring U.S. Sen. Joe Lieberman’s seat.

At issue is an ad the campaign began running last week, which featured voters who said they were supporting both McMahon and President Barack Obama, a Democrat. McMahon has endorsed Republican Mitt Romney in the presidential race. She appears in the ad only briefly, as a subtitle notes she approved the message.

The commercial seems to have upset Republican McMahon supporters, some of whom voiced their concerns in the comment section of the candidate’s Facebook page.

“You just lost my vote endorsing Obama,” one Facebook user posting as Mark Gery said in the comment section of a recent picture of McMahon on a jobs tour.

“I REALLY didn’t like her ads about Obama votes who were voting for her as well. If she is so attached at the hip with the Obama administration that she would put out an ad like that, I’ll leave her slot blank,” another user posting as Ellen Collins said.

Comments like that have been so numerous that McMahon’s staff has posted the following statement more than a dozen times in response:

“Linda actively supports Governor Romney. The ad is Democrats explaining that they are going to vote for Linda on the Independent party line. There are thousands of Democrats and Independents who are supporting Linda over Chris Murphy because she is a job creator, not a professional politician.”

McMahon’s spokesman Todd Abrajano said there was no way to be sure who the Facebook commenters are.

“For all I know Congressman Murphy could be sending his supporters over there to make hay,” he said.

But Facebook isn’t the only place Republicans are letting their feelings about the ad be known. Jerry Labriola, the state Republican Party chairman, said Republicans have been calling state central with their concerns. He said it’s generated the highest volume of calls he’s seen since becoming chairman.

“I’m working as hard as I can for our Republican ticket,” Labriola said. “I believe Gov. Romney’s pro-economic growth message is resonating and he can still win Connecticut. Other than that, I have no comment.”

Abrajano said all the supporters the campaign has talked to are savvy enough to see the purpose of the ad, which is to let Democrats know it’s alright to vote for both Obama and McMahon. He said a Republican can’t win a statewide election in Connecticut without the support of some Democrats.

“The numbers just don’t add up,” he said. “The people we’ve talked to, they understand what the ad is about and they understand that in order for Linda McMahon to win on Election Day she’s going to need a coalition of Republicans, independents, and Democrats.”

While a commercial encouraging ticket splitting seems counter-intuitive, the general election has never been about party affiliation for McMahon, who refers to herself as an “independent thinker” more often than as a Republican.

Vin Moscardelli, a political science professor at the University of Connecticut, said that while he was surprised by how explicitly the ad lays out its message, its general purpose reflects the reality of running as a Republican in a state Obama will almost surely win.

“She has to limit the extent at which people who turn out to cast votes for the president also cast votes for down-ticket candidates like Murphy,” he said. “This is effectively what she’s been asking people to do all along because no one really expects Gov. Romney to win Connecticut.”

Though the commercial does risk alienating Republican voters, Moscardelli said it might be a risk worth taking.