This poll shows the huge problem for Republicans trying to drop Trump at the convention

Republican elites may be increasingly confident that a contested convention can stop Donald Trump — but many of their voters aren't at all keen on the idea.

A new Vox/Morning Consult poll finds that 55 percent of self-identified Republican voters respond negatively to the idea that the candidate in first place after the primaries could lose the nomination at the convention. Only 35 percent reacted positively to that possibility.

We also asked GOP voters how they'd feel if it were Donald Trump specifically who lost the nomination in that way, and the breakdown of responses was quite similar — 56 percent felt negatively about this prospect, and 37 percent felt positively.

Furthermore, the most common emotions Republican voters said they'd feel about each of these scenarios were anger, disappointment, and frustration.

The findings bolster Trump's argument that if he does win the most delegates but falls short of a majority, there would be an outraged backlash. "If you disenfranchise those people, and you say, ‘Well, I’m sorry, but you’re 100 votes short, even though the next one is 500 votes short,’ I think you would have problems like you’ve never seen before," the billionaire said last month.

As for Republican elites' dreams that a contested convention could simply nominate someone who didn't even run for president — this got the most negative reaction of all. Sixty-three percent of Republican voters in our sample responded negatively to this idea, compared with only 27 percent who responded positively.

All this goes to show that the only plausible remaining option for stopping Donald Trump will be a tough sell to the party's voters indeed.

How the poll was set up

Our poll was conducted online by Morning Consult and surveyed 2,004 registered voters nationally. But for the purposes of this analysis, we're focusing on the views of both self-identified Republicans and self-identified supporters of the three remaining Republican candidates.

First, we asked a background question reminding respondents that if no candidate gets a majority of delegates the convention will determine the nominee, and asking them how much they had heard or read about this possibility on the Republican side this year. Among GOP voters, 31 percent said they'd heard a lot about it, 39 percent said they'd heard some, 16 percent said not much, and 14 percent said nothing at all.

Then we outlined various contested convention scenarios — first abstractly, without naming candidates, and only later naming Ted Cruz and Trump — and asked respondents how they would feel if these scenarios came about.

They were given a list of 11 different emotions to choose from, some of which we're counting as positive responses and others as negative. They are:

• Positive: "happy," "relieved," "excited," "proud," "hopeful," "interested"
• Negative: "disappointed," "angry," "frustrated," "helpless," "bored"

For each scenario we described, respondents could choose one of these options, all, none, or say they weren't sure. You can check out our coded results here, or the full toplines and crosstabs at Morning Consult Intelligence.

Our results

As mentioned above, 55 percent of the Republican voters in our sample chose a negative emotion to describe how they'd feel if "the candidate who has the most delegates based on voting from primaries and caucuses does not win the nomination at the convention." Thirty-five percent chose a positive emotion.

The top negative responses offered were "angry" (17 percent of Republicans), "disappointed" (15 percent), and "frustrated" (15 percent). In contrast, the top positive reaction was "interested" (11 percent), which, well, isn't all that positive. "Relieved" came in second (7 percent).

In the abstract, even most Ted Cruz supporters disliked this scenario, with 35 percent responding positively and 53 percent responding negatively. Trump supporters strongly disliked it (20-71). Most John Kasich supporters, however, were on board, with 51 percent reacting positively and 36 percent negatively.

When we named Donald Trump specifically as the candidate who'd lose out, the topline breakdown of responses from Republicans was quite similar: 56 percent responded negatively and 37 positively.

However, the breakdown of opinion among the various candidates' supporters shifted in predictable ways:

• Trump supporters turned further against the idea, moving from 20-71 to 17-78.
• Cruz supporters grew to like the idea, flipping from 35-53 to 52-41.
• Kasich supporters became even more enthusiastic, moving from 51-36 to 61-27.

Still, it is worth noting that even when Trump is named, Cruz supporters aren't overwhelmingly thrilled by the idea of deposing him if he finishes first.

Republican voters really don't like the idea of nominating someone who didn't run

We also checked what our sample thought of two other contested convention scenarios: that the second-place finisher in the primaries could emerge with the nomination, or that someone who didn't run at all could end up crowned the nominee.

Both were unpopular. But, as you can see in the chart above, the latter was far more unpopular. Sixty-three percent of Republicans responded negatively to this scenario, and only 27 percent responded positively. (Not surprisingly, large majorities of both Trump and Cruz supporters hate the idea that the convention could pick someone who didn't run for the nomination.)

The top negative responses offered were "angry" (25 percent of Republicans), "disappointed" (13 percent), "frustrated" (13 percent), and helpless (8 percent). And again, the top positive reaction was "interested" (8 percent).

As for the scenario in which the second-place person in the delegate count ends up winning, we tested this first generally, and then with Ted Cruz named specifically. This didn't change much on the toplines among Republicans — they went from 38-51 in the abstract to 42-50 with Cruz named.

However, once again, the breakdown of opinion among the various candidates' supporters shifted opportunistically after Cruz was named.

• Cruz supporters suddenly grew to love this idea, flipping from 46-42 to 73-21.
• Trump supporters turned further against the idea, moving from 26-66 to 21-71.
• And some Kasich supporters soured on it, moving from 45-40 to 42-48.

Overall, we'll need more research to get a better idea of just what voters will make of this unusual contested convention scenario. But our first pass at it indicates that deposing the first-place finisher could be difficult for voters used to the modern primary system to swallow.