President Barack Obama has come under fire over his defence on Friday of a developer's right to build a mosque blocks from Ground Zero in New York.
Republicans said Mr Obama was out of step with America on the project.
"It's unwise to build a mosque a the site where 3,000 Americans lost their lives as a result of a terrorist attack," Senator John Cornyn said.
On Saturday, Mr Obama said he was backing the rights of the developers, not the "wisdom" of the project.
Since a New York developer announced plans to build a 13-storey Islamic community centre and mosque about two blocks from the former World Trade Center site, prominent Republican politicians and a host of conservative pundits have attacked the project.
At a White House dinner celebrating Ramadan on Friday, Mr Obama vigorously defended the developers' right to put the mosque there "in accordance with local laws and ordinances".
Muslims "have the same right to practice their religion as anyone else in this country", the president said.
But on Saturday Mr Obama clarified his comments, saying: "I was not commenting, and I will not comment on, the wisdom of making a decision to put a mosque there."
Nevertheless, a number of opposition Republicans hit out at the president's stance on the US Sunday talk shows.
"It's unwise to build a mosque at the site where 3,000 Americans lost their lives as a result of a terrorist attack," Senator John Cornyn of Texas said on Sunday on Fox News.
"And I think to me it demonstrates that Washington, the White House, the administration, the president himself seems to be disconnected from the mainstream of America."
Meanwhile Ed Rollins, a veteran Republican campaign consultant, said Democratic candidates would be forced to take a position on the issue in campaigning for November's US mid-term elections.
"Intellectually, the president may be right, but this is an emotional issue, and people who lost kids, brothers, sisters, fathers, what have you, do not want that mosque in New York, and it's going to be a big, big issue for Democrats across this country," he said on CBS's Face the Nation.
"Every candidate who's in the challenge districts are going to be asked, how do you feel about building the mosque on the Ground Zero sites."
The White House and the president's supporters have sought to frame the Mr Obama's comments as a matter of conscience, not poll numbers, and argue that Republicans are inappropriately politicising the issue.
"This wouldn't be a controversy if it was a proposal to build a synagogue or a church," Democratic party chairman Tim Kaine said on CBS. "We don't prefer people and we don't punish people based on their religion."
The Politico website quoted a senior administration official as saying: "When I start to view religious freedom through the prism of midterm elections, I'm just going to quit."
While polling suggests a majority of Americans oppose plans to build the mosque, a Fox News poll released on Friday suggested 61% supported the developer's right to build the mosque.
"It was a bold decision - Obama could have stayed out of what is ostensibly a local matter," wrote polling analyst Nate Silver on the political website FiveThirtyEight.com.
"But a careful evaluation of the polls reveals it to be less politically risky than it might at first appear."