Trump's proposal came the day after President Obama's Sunday night televised address from the Oval Office in which the president urged Americans to reject discrimination against Muslim Americans.
"I wrote something today that I think is very very salient, very important and probably not politically correct, but I don't care," Trump said at a rally on an aircraft carrier-turned-museum in South Carolina.
The statement earned him a standing ovation at an event in which two protesters were led out. Trump called for "a total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on."
He cited polls as evidence of "hatred" of Americans by large segments of the Muslim population. One was a survey from Pew Research. He didn't include specifics, so it's not clear what the data there really show.
A 2011 Pew Global Attitudes survey found majorities of Muslims in other countries described Westerners as "selfish," "violent" and "arrogant."
"The polling firm has found that Muslims across the globe are overwhelmingly opposed to the Islamic State and in 2007 that Muslims were much less likely to view suicide bombings as justified than five years prior. Pew also found a partisan split in which Republican Americans were far more likely to hold negative views of Muslims than Democrats. In 2011, they learned that U.S. Muslims almost never consider suicide bombings to be justified."
At his rally, Trump then went on to highlight another poll.
"This was from the Center for Security Policy, very highly respected group of people, who I know, by the way — 25 percent of those polled agreed violence against Americans is justified. It's Muslims — 25 percent," Trump said.
The poll is highly suspect. Its methodology is questionable — polling online — and its questions in many cases are leading.
There may be a reason for that. While Trump calls the group "highly respected," it's a hawkish, ultra-conservative organization whose website features prominent warnings about the rise of Sharia, or Islamic law, in the U.S. and about the Muslim Brotherhood infiltrating this country.
"The Muslim Brotherhood agenda for the United States demonstrably seeks through subversive infiltration of American institutions the triumph of shariah," the group's president and founder Frank Gaffney writes on the website about a book he endorsed as part of its "Civilization Jihad Reader Series." He continued, "We are now on notice that U.S. Council of Muslim Organizations is simply the leading edge of the jihadist movement in this country. While the USCMO seeks to cloak itself in red, white, and blue, it is only for the purpose of accomplishing what can aptly be described as 'Star Spangled Shariah.' "
Gaffney is known for alleging the infiltration of the Muslim Brotherhood into the U.S., including Grover Norquist of Americans for Tax Reform. Gaffney even has a petition page set up on his group's website seeking to kick Norquist and Suhail Kahn out of the American Conservative Union and accusing them of "running influence operations against conservatives on behalf of the Muslim Brotherhood and other Islamist causes."
Reaction from other GOP presidential hopefuls came quickly. Ben Carson tried to draw this line: "Everyone visiting our country should register and be monitored during their stay, as is done in many countries," spokesman Doug Watts said. "We do not and would not advocate being selective on one's religion."
Others all-out rejected Trump's proposal.
Ted Cruz, who is competing with Trump for both the Tea Party and the evangelical vote, spoke to NBC News. "No, that is not my policy," he said. "I believe the focus should be on radical Islamic terrorism."
Jeb Bush called Trump "unhinged."
Marco Rubio said Trump's plan was outlandish and offensive.
Chris Christie said Trump has no idea what he's talking about.
Former Vice President Dick Cheney was asked about it during an appearance on the Hugh Hewitt Radio program.
"Well, I think this whole nation, that we can say, 'No more Muslims,' that we can just ban a whole religion, goes against everything we stand for and believe in," he said.
Muslim civil rights groups, meanwhile, reacted with alarm. Nihad Awad of the Council on American-Islamic Relations said Trump sounded like the leader of a lynch mob.
"If such hatred and bigotry is not outright rejected by the GOP, then it will be part of its legacy for many years to come," Awad said.
Republican Party chairs in two key early primary states, South Carolina and New Hampshire, did outright reject it.
But a co-chairman of Trump's state veterans coalition in New Hampshire defended Trump's statement, arguing that it's the same policy used against Japanese-Americans during World War II.
"What he's saying is no different than the situation during World War II, when we put the Japanese in camps," state Rep. Al Baldasaro said, per WMUR's John DiStaso. "The people who attacked innocent people in Paris came through open borders. From a military mind standpoint, all Donald Trump is saying is to do what needs to be done until we get a handle on how to do background checks."
Baldasaro also called on Jennifer Horn, the state party chairwoman, to step down for calling Trump's plan "un-American."
"She needs to resign because she has no clue," Baldasaro said. "She's my friend, but I have to separate that from the Republican Party."
As divisive as this policy is, Trump did something else last night — something he always does at his rallies: portray himself as the man to unify the country.
"Wouldn't it be good for all of us to really get together and make our country great again?" Trump asked, invoking his slogan. "Isn't that what we really want to do?"