Public opinion has since swung back in favor of compromise, but a sizable chunk of Republicans still seem hesitant to embrace it.

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A January Monmouth University poll found that 54 percent of GOP voters say the problem in Washington is more about not enough politicians being willing to stand for their principles, while 45 percent said the problem was not enough politicians willing to compromise. Among Democrats, it's the opposite.

GOP voters' preference for conservative purity over deal-making has perhaps never been clearer than in this presidential race. Donald Trump's often-extreme views on hot-button issues like immigration and refugees are far from any middle ground with the other side. (Democrats most likely wouldn't even entertain the idea of negotiating about whether to temporarily ban Muslim immigrants from America, for example.)

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So it's particularly interesting, then, that Trump is one of the most vocal candidates in the entire 2016 campaign when it comes to the benefits of compromise — or, to use Trump's own language, making deals.

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Trump, in fact, has been talking a lot lately about how well he gets along with with Democratic leaders in Congress and even bragging about the deals he'd cut with them while president. In doing so, he's drawing a direct contrast with his rival, Sen. Ted Cruz (R-Tex.), who is very much opposed to shaking hands with the other side — and often even his own party's leaders.

Listen to what Trump had to say in Saturday's ABC News debate in New Hampshire. Co-moderator Mary Katharine Ham asked Trump whether the deal-making extolled in his book, "The Art of the Deal," would be a liability among Republican voters who "are sick of the deal-making currently going on in Washington."

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Trump answered with an unabashed "no."

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"A good deal-maker will make great deals," he said.

He went on: "With Congress, you have to get everybody in a room, and you have to get them to agree. But, you have to get them to agree with what you want, and that's part of being a deal-maker. You can't leave the White House, go to Hawaii and play golf for three weeks and be a real deal-maker. It doesn't work that way. You have to get people in, grab them, hug them, kiss them, and get the deal done. But it's got to be the deal that you want."

The message here is clear: Trump's ability to make a deal is so unequivocal that, when he strikes one, Washington will work again. In other words, there's no need to be opposed to compromise, conservatives, when President Trump is in the White House. It'll work out in your favor.

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You could argue Trump isn't talking about compromise here so much as convincing the other side to agree to his terms. But still, a GOP front-runner praising the benefits of hugging and kissing members of Congress is a striking contrast to where the Republican electorate stands on compromise — and to some of his competition.

Trump's most formidable opponent is popular precisely because he opposes deals. Cruz has gone to war with leaders in his own party no fewer than five times. On the campaign trail, he brags about the budgets and bills he's stopped in their tracks — albeit most of them just temporarily.

"I will acknowledge that, when I’m in the Senate dining room, I’ve sometimes wondered if I need a food taster," Cruz told a laughing Iowa crowd recently.

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Trump, meanwhile, is trying to turn Cruz's obstructionist tendencies into a liability:

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"We have a system. The founders created a system that actually is a very good system; it does work," he said on MSNBC's "Morning Joe" less than a week before the Iowa caucus. “But it can’t work if you can get nobody to go along with you, and that’s the problem that you have with Ted Cruz. He’s a guy that nobody likes and nobody trusts, and he is a nasty guy. He says things that are very nasty."

But given the polling, it would seem Trump's new strategy is risky. He's gambling that voters will trust him enough to know his version of deal-making will be much different than what's going on in Washington right now.