Donald Trump

Republican presidential candidate, businessman Donald Trump, speaks during a rally coinciding with Pearl Harbor Day at Patriots Point aboard the aircraft carrier USS Yorktown in Mt. Pleasant, S.C., Monday, Dec. 7, 2015. (AP Photo/Mic Smith)

Donald Trump's incendiary - and likely unconstitutional - suggestion that the U.S. prevent Muslims from entering the country has set off a firestorm with criticism from both Democrats and Republicans.

That hasn't slowed Trump, who is leading the GOP presidential pack.

"We have no idea who's coming into our country," Trump said during a Monday night campaign rally in South Carolina. "We have no idea if they love us or they hate us. We have no idea they want to bomb us. I have friends who are Muslims, they're great people. They know we have a problem.''

In announcing his proposal, Trump cites a poll from the Center for Security Policy showing a 25 percent of the Muslim population agreed that violence against Americans is justified as a part of the global jihad. Those findings are controversial, but another poll shows many Americans likely believe they are true.

The Public Religion Research Institute 2015 American Values Survey found that 56 percent of Americans said the values of Islam are at odds with American beliefs and way of life. Almost six in 10 white Americans feel that way, as compared to 48 percent of blacks and 46 percent of Hispanics. The highest percentage of those that agree with the statements are white evangelical Protestants, 73 percent of whom said Islam is incompatible with the U.S. way of life, though a majority of every Christian religious group said they feel the same.

People's feeling on the matter are strongly influenced by their political leanings, the poll shows. Three-quarters of Republicans (76 percent) and 77 percent of Tea Party members think Islam is at odds with the American way of life. While the poll shows support among other political groups is smaller, it's still considerable: 57 percent of independents and 43 percent of Democrats agree that Islam is incompatible with life in the U.S.

Trump's response

Republican National Committee chair Reince Priebus has made it clear he doesn't support Trump's plan.

"We need to aggressively take on radical Islamic terrorism but not at the expense of our American values," he said Tuesday.

Trump, who has gambled on controversial statements before only to further his lead in the polls, doesn't appear to be backing down, however.

"I wrote something...that I think is very, very salient, very important and probably not politically correct, but I don't care," he said.