Over the past week, Donald Trump's inflammatory remarks about Mexican immigrants have enraged the Hispanic community, cost him million-dollar business contracts and dominated media coverage of the 2016 presidential race.

But the overall reaction from much of the rest of the Republican field has ranged from tepid criticism to, in at least one case, strong words of support.

Trump has put the rest of the GOP in a difficult position with his assertions that Mexico was sending "rapists," killers and drug dealers across the border into the United States. While most of the candidates would rather pretend Trump doesn't exist, the remarks -- and his refusal to disavow them -- have made that impossible.

The celebrity TV host and businessman has succeeded in sucking much of the oxygen out of campaign coverage, and he swings harder each time he's knocked back. On Wednesday night, CNN's Don Lemon noted in an interview with Trump that a study cited by the candidate to bolster his argument actually referred to Central American immigrants who were raped while in Mexico, not in the United States.

Trump responded: "Well, somebody's doing the raping, Don! I mean somebody's doing it! Who's doing the raping?"

Such rhetoric does little to help Republicans seeking to connect with Hispanic voters, a demographic they need to win a national general election. But the candidates are also cognizant that Trump is tapping into a bloc of conservative GOP primary voters who welcome his abrasive approach and share his attitude over illegal immigration; he has surged to second place in several polls nationally and in early-nominating states.

So far only long-shot former New York Gov. George Pataki -- desperate for some attention himself -- has taken a proactive approach, sending a letter to the rest of the GOP field on Wednesday asking them to join him in denouncing Trump and his comments.

"As Donald Trump doubles down, I’m asking you to join me in standing up," Pataki wrote.

Trump responded in typical Trump fashion:

Other GOP candidates have only commented when asked to respond to Trump's remarks. And Sen. Ted Cruz (R-Texas), who is angling for the same voters as Trump, came to Trump's defense.

Cruz is not alone: a number of other prominent conservatives, including National Review editor Rich Lowry, Iowa Rep. Steve King and American Conservative Union chairman Matt Schlapp, have mounted at least limited defenses of Trump's overall immigration message.

Kevin Madden, a former campaign strategist for Mitt Romney, said some of the other GOP candidates could benefit from confronting Trump head-on in a way that could draw new voters to the Republican party.

"There is a sliver of the electorate right now who love this blustery, celebrity-driven showmanship," Madden said. "But I think a lot bigger bloc is shopping around who would be drawn to a candidate who would confront such offensive rhetoric."

It's possible the candidates don't want to risk a tussle with Trump, a ferocious adversary when poked. Or maybe they're waiting for a larger public forum, like the debate stage, to confront him face-to-face.

For now, they seem to be toeing a careful line -- distancing from his offensive comments but also not alienating themselves from his broader anti-illegal immigration message.

Last weekend, former Florida Gov. Jeb Bush, whose wife is Mexican-American, was asked in Spanish about Trump at an event in Nevada. In Spanish, he said that Trump doesn't represent the values of the Republican Party, according to Bloomberg News.

Asked again in English, Bush said, "I don't agree with him. I think he's wrong. It's pretty simple."

Former Texas Gov. Rick Perry had a similar response during an appearance at the National Press Club on Thursday: "Let me say, I do not think Donald Trump's remarks reflect the Republican Party. I think the Republican Party is reflected in people like me." Several hours later his campaign sent a press release touting an even stronger Perry response to Trump during a Fox News interview.

New Jersey Gov. Chris Christie, campaigning in New Hampshire this week, said Trump's comments were "inappropriate and have no place in this race." Sen. Lindsey Graham (S.C.) said in response to a question at a campaign event in Iowa, "I don't need a letter from Gov. Pataki. I said from day one, when you label a group of people as rapists and drug dealers, says more about you then it says about them.”

Trump's campaign manager, Corey Lewandowski said he hadn't seen any of the remarks from the other candidates and wasn't concerned "in any way shape or form" with what the other candidates are doing.

Chuck Laudner, Trump’s top campaign operative in Iowa, who backed that state’s caucus winner Rick Santorum in 2012, said proudly that Trump is the ultimate establishment irritant.

“They can’t control that debate,” he said in an interview prior to the blow up over Trump's remarks on Mexicans. “They’ve lost total control when Trump is in the room. They can make Rick Santorum change his opinion on an issue. Can’t do that with Trump. They’re screwed.”