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Two-thirds of Iowa’s Republican voters say they would definitely vote to re-elect Trump if the general election were held today, but nearly as many say the state’s party ought to welcome challengers to the President to Iowa’s first-in-the-nation caucuses, according to a new CNN/Des Moines Register/Mediacom poll.

The President’s strength among the state’s registered Republican voters is clear in the poll, with Trump earning an 81% approval rating, a 77% favorability rating, and majorities heralding his choices on immigration, judicial appointments, tax cuts, tariffs and even firing his attorney general as good moves. And by a better than two-to-one margin, Republican voters in Iowa place more blame on congressional Republicans (54%) than on the President (24%) for the party’s recent midterm losses.

RELATED: Full poll results

There is one topic on which Iowa Republicans seem strongly critical of Trump’s choices: his use of Twitter. About seven in 10 (72%) say the President has erred by posting potentially inflammatory messages on Twitter on a regular basis. On each other issue position tested in the survey, majorities say the President made a good move.

Overall, 67% of registered Republicans say they would definitely vote to re-elect Trump if the election were held today, 19% would consider someone else and just 10% of the state’s Republicans say they would definitely vote for someone else.

Republicans in Iowa are fairly closely divided on whether they feel more of an allegiance to the President (37%) or to the Republican Party (43%). Another one in five are unsure which they are closer to. But most (55%) say they think the President cares more about people like them than about people like himself (26%).

Just a quarter (26%) say the Iowa Republican Party should discourage challengers to the President, while 63% feel the party ought to welcome them.

The share in favor of welcoming challengers is higher among Iowa Republicans with college degrees (72%) than among those without degrees (56%). It’s also higher among women (66%) than men (60%), and among younger Republicans (67% among those under age 45) than older ones (60% age 45 and up feel that way). And those who consider themselves “very conservative” are far less apt to want the party to welcome challengers (47%) than those who are less conservative or moderate. Those differences correspond with stronger support for Trump in some cases – gender and ideology, notably – but not all.

The overall welcoming posture doesn’t mean the state’s GOP is particularly welcoming to those who have been critical of Trump, however.

Iowa Republicans are more likely to have positive views of those political figures who at times have been warmer to Trump than of those who are routinely critical. Texas Sen. Ted Cruz, Florida Sen. Marco Rubio and soon-to-be Utah Sen. Mitt Romney, Republicans who were one-time critics of the President but have been publicly supportive of him at other times, all have broadly favorable ratings in the poll. Those who have been more overtly and consistently critical, including outgoing Sens. Jeff Flake and Bob Corker and outgoing Ohio Gov. John Kasich, are less positively viewed.

Those Iowa Republicans who say they feel more allegiance to Trump than to the party have a particularly negative take on the President’s Republican critics. Twenty-three percent have an unfavorable view of Corker, compared with just 4% among those who feel a closer tie to the party. On Flake, nearly half of those who feel a close tie to the President (46%) have a negative view, compared with 13% of those who feel closer to the party. And the divide is nearly as large on Kasich, with 43% of those who feel closer to the President viewing him unfavorably, compared with 12% among those who feel closer to the party.

Looking to the presidential prospects of those Republicans who could potentially make a run in the future, just two of the seven potential candidates tested have a majority of Iowa Republicans saying they would ever consider backing them for president – 59% say they could support Rubio, 53% Romney. And there are more who would consider a Nikki Haley candidacy than would rule it out (46% would ever consider it, 21% would never support it).

There’s more opposition than support, however, for presidential runs from Kasich (39% say they would never back him, while 31% say they would consider it), Flake (47% never to 14% ever) or Corker (40% never to 11% ever). Iowa Republicans also tilt against Ben Sasse, a Republican senator from neighboring Nebraska, with 31% saying they would never vote for him and 21% saying they would ever consider it.

The CNN/Des Moines Register/Mediacom poll was conducted by Selzer and Co. from December 10 through 13 among a random sample of 450 registered Republican voters reached on landlines or cellphones by a live interviewer. Results for the sample of Republican voters have a margin of sampling error of plus or minus 4.6 percentage points; it is larger for subgroups.