Everybody loves Gabby Giffords — just not necessarily on the campaign trail.

When the gun control advocacy group led by the former congresswoman from Arizona threw its support behind several endangered Senate Democrats in Western and Southern states, the candidates carefully moved to distance themselves from the affable Ms. Giffords and boasted about their strident defense of Second Amendment rights.

The message was clear: Thanks, but no thanks.

The candidates — Sen. Mark Udall in Colorado, Sen. Mary L. Landrieu in Louisiana, Sen. Kay R. Hagan in North Carolina and Rep. Bruce L. Braley, vying for Iowa’s open Senate seat — have tried to avoid the gun debate in key races that will determine whether their party keeps its majority in the U.S. Senate.

Ms. Giffords, who survived a gunshot to the head by a deranged assailant three years ago at an event in her congressional district in Tucson, remains a sympathetic figure. But as a leading advocate for gun control measures, her support could do more harm than good for Democrats in firearm country.

Political strategists warn that the gun issue posses too much of a risk for Democrats already struggling in those red and purple states. It threatens to stir up opposition among Second Amendment advocates who could swing a close election to the Republican candidate.

The gun issue is particularly vexing for Mr. Udall in Colorado, where two Democratic state senators were booted from office in recall elections last year after backing tough gun control measures passed by the Democrat-run legislature.

“Democrats are doing everything they can to stay away from it,” said Denver-based pollster and political analyst Floyd Ciruli. “To the extent that any advertising from the gun control forces got out there, I think Udall would be very nervous that there’s more downside risk than upside.”

An activist in Ms. Giffords’ Americans for Responsible Solutions PAC said the group is “fully aware” of the potential to hurt Democrats they try to help.

“It’s something we think about a lot,” said the activist, who spoke privately about the internal deliberations at ARS. He said the group’s research shows that publicizing gun issues motivates gun control supporters and persuades people to join the cause, especially among female voters.

Some Democratic strategists viewed Ms. Giffords as an asset for Mr. Udall and the party’s other vulnerable candidates in pro-gun states.

“She’s a Westerner. She’s a gun owner. She understands Western issues,” said Jill Hanauer, president of Project New America, a Democratic political consulting firm that got its start focusing on Western states.

“America is having a long-awaited conversation about gun safety,” she said.

Al Gore’s support of gun control has been blamed for his narrow loss to George W. Bush in the 2000 presidential election. Ever since, Democrats have been retooling their message on firearms and gun violence with varying degrees of success.

A rash of deadly shooting sprees and President Obama’s push for tougher gun laws have rekindled the firearms debate. A Rasmussen Reports poll last week placed gun control among the top 10 issues for voters.

“Some of these races look like they could be so close that just about anything could matter,” said Christopher Mann, a political science professor at Louisiana State University who specializes in campaigns and voting behavior.

“If the debate becomes about gun control, that is not where Mary Landrieu wants the debate to be about. Mary Landrieu wants a very different debate,” he said. “If she is trying to win a Senate race talking about gun control, she’s losing.”

He stressed that ARS could minimize backlash from gun rights voters by avoiding TV ads and targeting direct mail and robocalls at households identified as sympathetic to its message.

Ms. Landrieu’s campaign did not respond to questions about gun policy and support from ARS.

While pushing away from Ms. Giffords, these Democrats also will have to fend off attacks from gun rights groups.

“We are going to be butting heads [with Giffords’ group] in all those races,” said Larry Pratt, executive director of Gun Owners of America. “It will energize our people, I’ll tell you that.”

The National Rifle Association’s political arm has begun rallying opposition to Ms. Hagan and Ms. Landrieu, saying first lady Michelle Obama endorsed them as “critical” to enacting Mr. Obama’s gun control agenda.

When asked about the gun issue, the Udall campaign pointed to the senator’s vote against legislation that would have reinstated a ban on military-style rifles or assault weapons.

“Mark has long supported Colorado’s hunters, sportsmen, and gun owners,” he said. “Responsible gun ownership is part of our Western heritage, and Mark has always supported this through his work to expand public shooting ranges and his successful efforts to stop overbroad bans on common hunting rifles.”

All of the candidates backed by the Americans for Responsible Solutions PAC voted for a Senate bill last year that would have expanded background checks for firearm purchases. The bill’s defeat ended Mr. Obama’s push for more gun laws in response to the elementary school shooting spree in Newtown, Conn., that left 20 children and six adults dead.

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