WASHINGTON  The top Republican in charge of Senate campaigns said Sunday that President Obama's support of a Muslim group's right to build an Islamic center near the site of the 9/11 attacks in New York would become an issue in the fall elections.

The comments from Sen. John Cornyn, R-Texas, chairman of the National Republican Senatorial Committee, added to the firestorm that erupted this weekend over Obama's decision to first weigh in on the controversy and then clarify that he was not endorsing the site for the center.

The proposed $100 million project, two blocks from the World Trade Center site, would include a community center, a mosque and memorial to 9/11 victims. A city commission unanimously approved the project this month.

THE OVAL: Obama makes proposed mosque in New York a national issue

On Sunday, some Republicans called Obama out of touch for supporting the rights of a developer and Imam Feisal Abdul Rauf to build the center. Obama's critics echoed statements made by House Minority Leader John Boehner and former GOP vice presidential nominee Sarah Palin.

"It's unwise to build a mosque at the site where 3,000 Americans lost their lives as a result of a terrorist attack," Cornyn said on Fox News Sunday. "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."

Voters, Cornyn said, will "render their verdict" in the fall.

Rep. Pete King, R-N.Y., a staunch opponent of the project, accused Obama of "trying to have it both ways" and said the president "should have been much more clear, much more precise."

Obama said Friday that he understood the emotions surrounding the planned Islamic center, but people of all faiths are welcome in the USA and must not be treated differently by the government.

"As a citizen, and as president, I believe that Muslims have the same right to practice their religion as everyone else in this country," Obama said. "And that includes the right to build a place of worship and a community center on private property in Lower Manhattan, in accordance with local laws and ordinances. This is America."

The president sought to clarify his remarks Saturday, saying he was not commenting on "the wisdom of making the decision to put a mosque there."

Rep. Chris Van Hollen, D-Md., chairman of the Democratic Congressional Campaign Committee, said Sunday on CNN's State of the Union, that it would "be wrong to politicize the issue" and that he supported Obama.

New York Mayor Michael Bloomberg agreed with Obama, issuing a statement Friday calling the issue an important test of the separation of church and state. Bloomberg called Obama's statement a "clarion defense of the freedom of religion."

White House spokesman Bill Burton said Saturday that Obama's clarification does not mean he is backing off his Friday comments.

"What he said last night, and reaffirmed today, is that if a church, a synagogue or a Hindu temple can be built on a site, you simply cannot deny that right to those who want to build a mosque," Burton said.