As Republican candidates across the country seize on the proposed construction of a mosque near New York's Ground Zero as a campaign issue, some influential figures in the GOP are growing concerned that it could backfire.

Although public opinion is running overwhelmingly against the construction of the Islamic center, Republican strategists said there are dangers in pushing the issue too forcefully.

Pollster David Winston, who advises GOP congressional leaders, worries that the mosque controversy could overshadow the issues voters care about most. "While this is certainly an issue that has generated a lot of emotion, when it comes to voting, the election is going to be about the economy and jobs," he said.

Others fear that the party risks appearing intolerant of religious differences.

"One of the biggest dangers in politics is to overplay an issue," said former Republican National Committee chairman Ed Gillespie, who warned that voters could conclude that Republicans who oppose the New York mosque are taking a stand against Islam in general. "It's very important that, as Republicans talk about this issue, we be thoughtful and careful about making those distinctions," he said.

Yet some of the party's most visible figures have taken the opposite approach in reaction to President Obama's declaration that Muslim Americans have a right to build the center.

Former House speaker Newt Gingrich (Ga.) told the Fox News Channel that building a mosque so close to where terrorists killed thousands of Americans would be like putting a Nazi sign next to the Holocaust Memorial Museum. On the same network, former Alaska governor Sarah Palin warned: "This is an insensitive move on the part of those Muslims who want to build that mosque in this location. It feels like a stab in the heart to, collectively, Americans who still have that lingering pain from 9/11."

In congressional districts nationwide, hundreds of miles away from Ground Zero, Republican candidates have demanded that their Democratic opponents declare their positions on the mosque. Senate Majority Leader Harry M. Reid (D-Nev.) -- under pressure from his GOP opponent, Sharron Angle -- issued a statement on Monday saying he opposes the project.

Not all Republicans see an advantage in exploiting the controversy. New Jersey Gov. Chris Christie, a rising star in the party, declined to give his opinion. He said that Obama and some members of the GOP are "playing politics with this issue, and I simply am not going to do it."

"We have to bring people together," Christie added. "And what offends me the most about all this is that it's being used as a political football by both parties."

It was not all that long ago that Republicans considered Arab and Muslim Americans to be a potentially important voting bloc. In his 2000 campaign for president, Texas Gov. George W. Bush paid particularly close attention to their concerns. In his second debate with Vice President Al Gore, Bush criticized racial profiling of Arab Americans. He ultimately won the endorsements of various Muslim American organizations. Bush was also the first U.S. president to use the word "mosque" in his inaugural address.

Even in the days after Sept. 11, 2001, Bush made a point of visiting the ornate mosque on Washington's Embassy Row. But after the passage of the USA Patriot Act and other measures that heightened Muslim American concerns about civil liberties, their political support for him evaporated. And with his departure, the Republican Party's Muslim outreach effort gave way to assertions that Obama was too solicitous of the Arab world's opinion.

Strategists in both parties say that they think the issue will be all but forgotten by November.

"The support for criticizing a mosque is half a mile wide and an inch deep," conservative activist Grover Norquist warned. "And at the end of the process, the only people who will remember it are the people who feel threatened by this -- not just Muslims, but Sikhs, Jews, Hindus, Buddhists and Mormons."

Although there may be short-term political gain now from criticizing the mosque project, he said, the subsequent backlash and perception of religious intolerance may last a long time.

Staff researcher Julie Tate contributed to this report.