(AP) -- Amid fear of terrorism, Republican presidential candidates for months have escalated their rhetoric about the place of Muslims in the United States.

A Muslim shouldn't be president. Muslims fleeing war-torn Syria and Iraq should be barred from the country. Mosques should be placed under surveillance and shut down if people are radicalized in them.

Republican front-runner Donald Trump's call Monday for a "total and complete shutdown of Muslims entering the United States" was the latest salvo for a party aggressively testing the boundaries between concerns about security and discrimination against a religious group.

For most of Trump's rivals in the 2016 race, as well as numerous other Republicans, it was also the proposal that finally crossed that line.

"Donald Trump is unhinged," former Florida Gov. Jeb Bush said via Twitter. "His 'policy' proposals are not serious."

South Carolina Republican Chairman Matt Moore, whose state is third on the primary voting calendar, said that "as a conservative who truly cares about religious liberty, Donald Trump's bad idea and rhetoric send a shiver down my spine."

The nearly unanimous condemnation from fellow Republicans, Democrats and legal and immigration experts showed no sign of affecting Trump. He reiterated his proposal to keep Muslims out of the U.S. "until our country's representatives can figure out what is going on" at a Monday night rally in South Carolina and again in a round of television interviews Tuesday morning.

Trump has faced pushback from within his party for earlier comments about Muslims, but never with such speed and force.

Some rivals challenged his debunked assertion that thousands of Muslims living in New Jersey cheered the 9/11 attacks. The GOP field largely condemned his support for the idea of a database to track Muslims living in the U.S., but his comments were vague enough that Trump was able to walk them back without much harm to his campaign.

Trump's comments Monday came as his lead in preference polls in Iowa, the state that kicks off the nominating contest, appeared to be challenged by Texas Sen. Ted Cruz. If the real estate mogul's goal was to shift focus away from Cruz and back onto his candidacy, he no doubt succeeded.

Trump's comments seem aimed squarely at Republican primary voters wary of Muslims, particularly those with direct ties to countries in the Middle East that have spawned violent extremist groups.

A 2014 Pew Research Center poll showed Republicans view Muslims more negatively than they do any other religious group, and significantly worse than do Democrats. Following the Nov. 13 attacks in Paris, responsibility for which was claimed by the Islamic State group, surveys showed Americans increasingly opposed to accepting refugees from Syria, the predominately Muslim country where IS has a stronghold.

For Americans, the fear of Islamic State-inspired attacks drew even closer last week when a married couple killed 14 people in San Bernardino, California. The FBI said both had been radicalized for some time and the woman claimed allegiance to the Islamic State on Facebook shortly before the attack.

While Trump's rhetoric may be more bombastic and his proposals more aggressive, his rivals have proposed their own ideas for keeping tabs on Muslims in the United States and blocking those who want to come here.

In September, retired neurosurgeon Ben Carson said he did not believe a Muslim should serve as president of the United States. "I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that," Carson said in an interview with NBC's "Meet The Press."

Following the Paris attacks, which left 130 people dead and hundreds more wounded, GOP candidates rallied around proposals to limit Muslim refugees coming to the U.S. Their calls were echoed by Republican governors who vowed to keep Syrian refugees from being resettled in their states.

Cruz proposed legislation banning Syrian Muslims from coming to the U.S. Bush said American assistance to Syrian refugees should focus primarily on Christians. And Carson compared handling refugees fleeing Syria's intractable civil war to dealing with "rabid dogs."

After Trump said he wanted surveillance of "certain mosques" and would considering shutting down some of those houses of worship, Florida Sen. Marco Rubio said he, too, would be willing to shut down mosques and any other places that radicalize people.

While Trump has been at the forefront of his party's aggressive posture on Muslims, Democrats say the comments from other candidates give Democratic front-runner Hillary Clinton a ripe opportunity to cast the entire GOP field as out of step with American values of religious tolerance.

"Given how far he's pushed the party, Democrats, including Hillary Clinton, are going to have no problem tying all of the candidates to Donald Trump in one nice little extremist package bow," said Jim Manley, a Democratic strategist.

But for some Republicans, the most pressing challenge isn't keeping Trump from negatively branding Republicans in the general election -- it's making sure he's not the candidate representing the party in next November's White House race.

"So far, every boundary he has pushed has worked out for him," said Ari Fleischer, who served as White House press secretary for former President George W. Bush. "I hope GOP voters recognize this time he's gone too far."

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Follow Julie Pace on Twitter at: http://twitter.com/jpaceDC