Donald J. Trump has dominated the Republican Party for eight years, and our recent poll results show that he is dominating the Republican primary race again. So it’s not wrong to wonder whether Mr. Trump is simply undefeatable — even after his third criminal indictment.

But there was one moment — one fleeting moment — when it really did look like Republicans might move on. It was in the aftermath of the 2022 midterm election, when Mr. Trump’s party and his preferred candidates fared far worse than expected. It undermined the perception of his strength and dominance. He was a loser.

With that in mind, consider our first New York Times/Siena College survey of the Iowa caucus, released Friday. It is by no means a bad survey for Mr. Trump: He leads Ron DeSantis by a comfortable margin, 43 percent to 20 percent. Tim Scott sits even further back, at 9 percent.

But Mr. Trump’s position is unequivocally weaker in our Iowa poll than in our nationwide survey. His support is well beneath 50 percent in Iowa, and his opponents seem stronger. Mr. DeSantis has the highest favorability ratings in the poll, and clear majorities of likely caucusgoers consider him more “likable” and “moral” than the former president. Mr. Trump’s electability advantage over Mr. DeSantis is also far smaller — just 9 points — than it is nationwide.

A 23-point deficit is still a daunting gap for Mr. DeSantis. But unlike the national poll, our Iowa poll has revealed a few cracks in Mr. Trump’s armor. If Mr. DeSantis (or another challenger) could ever pry those cracks open and win the Iowa caucuses — the first nominating contest of the race — one wonders what kind of effect that might have on Republican voters.

After all, the only time Republicans were prepared to move on from Mr. Trump was the one time he and his supporters had to accept that he lost, after the 2022 midterm election.

A few other tidbits from our polling this week (moderately wonky)

• Will Hurd, the former Texas congressman, narrowly missed the qualifying threshold for the first G.O.P. debate on Aug. 23 in our national poll earlier this week. He had the support of 0.57 percent of Republican primary voters, near the 1 percent needed to help him qualify for the event (Mr. Hurd has not yet qualified for the debate; The Times is tracking who has qualified, here).Usually, 0.57 percent would be rounded to 1 percent, but while the poll was being conducted we decided that wasn’t appropriate for this survey. Republicans had set a 1 percent threshold to winnow the debate field; rounding to the nearest whole number didn’t seem like it was in the spirit of the cutoff for candidates in this case.

• Vivek Ramaswamy also had cause to be disappointed in our polls. He received 2 percent of the vote in our national survey, compared with about 6 percent in the FiveThirtyEight polling average and over 10 percent in some online polls. I’ll offer two basic theories for why he did worse in our poll.

  One is that it’s about survey administration: In an online survey, you see a long list of candidates, read them over, and then you choose one. In our phone survey, you either immediately volunteered your preference after hearing the question, or you heard a list of more than a dozen candidates and chose an answer at the end. If you’re an undecided voter, the online setting might help you find and choose someone you’re not especially familiar with. You may be overwhelmed on the phone, and even if you liked Mr. Ramaswamy when he was mentioned 20 seconds earlier, you could forget by the time the interviewer is done asking the question.

  A second possibility is that it’s about the kind of voters who participate in the big online panels that power so many polls today. Maybe they’re, shall we say, a little too online — and perhaps unusually likely to be aware of Mr. Ramaswamy’s campaign. My guess is that this is probably a factor: Online polls recruited by mail and by YouGov, the gold standard of this kind of polling, don’t show Mr. Ramaswamy doing so well, even though they were also conducted online.

• This Times/Siena national poll used an elaborate model of the likely Republican primary electorate, but it’s hard to say it made any difference in the result. Mr. Trump would have held a commanding lead with at least 50 percent of the vote no matter how we defined G.O.P. primary voters.

• The Democratic primary, however, is a case where more sophisticated modeling of the primary electorate might make a huge difference. While President Biden leads Robert F. Kennedy Jr. by a wide margin, 64 percent to 13 percent, among Democratic leaners, he enjoys a far wider lead — 74 percent to 8 percent — among those Democratic leaners who have ever actually voted in a primary, including 92 percent to 4 percent among those who voted in a Democratic primary in 2022.

  My guess: if we had done an elaborate Democratic primary poll — and we did not, in the absence of a competitive race — Mr. Biden’s lead would have grown.

• As I mentioned a few days ago, we’ve started to mull whether and how we can use respondents who begin to take our polls but don’t complete the interview. In our longer national surveys, about 15 percent of our respondents fall into this category, and they’re the kind of less educated and less reliable voters whom we want included in our polls.

  Interestingly enough, including these voters might have made a slight difference in our national poll this week. Rather than being tied, Mr. Trump would have led Mr. Biden by one point, 43 percent to 42 percent, if the survey had included respondents who decided to stop taking the survey before it was completed.

  It’s not clear whether this is just a random blip or indicative of a systematic tendency for these drop-off voters to back Republican candidates. Until now, we haven’t had the data necessary to fully evaluate this issue. In particular, we haven’t had the self-reported educational attainment of these respondents. But it’s something we’ve begun to track and may ultimately incorporate into our design.