Paul Ryan became something of a GOP rescuer last year after assuming the role of House speaker and uniting warring factions of his party. Well liked by constituencies both inside and outside of his party, Ryan is also something of a rare breed, so it's no surprise he is often mentioned as the ideal presidential candidate for struggling Republicans.

But the race for the White House is not the speakership contest. And even those who might like to see Ryan as the party standard-bearer would note that while he was able to unify the party to win the gavel, he hasn’t won a single vote or delegate. The emergence of the House speaker on the convention floor in Cleveland would be antithetical to the expressions of Republican voters.

“It’s not a politically healthy prescription for the message that is being sent right now from the country,” says Greg Mueller, a Republican strategist whose firm works for an anti-Trump super PAC.

The nomination of Ryan—or any candidate not in the running, for that matter—at the July convention is not only considered a Beltway fantasy for restless Republicans, but it would also be politically and practically damaging for the Wisconsin congressman and the party he is trying to fix, say political strategists.

“The idea that you have two candidates who have been through the fire, who, combined, get 70-plus percent, and you’re going to turn around and say, ‘Never mind them— we will pick someone who hasn’t run for a minute?’” says Norm Ornstein of the American Enterprise Institute. “I think you'd have Chicago 1968 all over again.”

Ryan, who will be the neutral chair of the convention, has denied interest in the idea to the point of exhaustion, even issuing a cease-and-desist letter to a group trying to draft him. Sources close to the speaker say he is doing nothing publicly or privately to promote the idea, which has been stirred up again recently by Karl Rove and others calling for a fresh face to bring the party back from the edge.

“I’m not the fresh face,” Ryan told Hugh Hewitt’s radio program on Monday, calling in from Israel while on his first overseas trip as speaker. “I think you need to run for president if you’re going to be president, and I’m not running for president. So period, end of story.”

Fellow Wisconsinite and Republican National Committee Chairman Reince Priebus said as much over the weekend during a slate of interviews, arguing that the eventual nominee will likely be one of the three current candidates: Donald Trump, Ted Cruz or John Kasich.

The Club for Growth, which has been actively working against Trump, also opposes the nomination of another candidate and believes it would damage the party.

"It's a bad idea for the party and a fantasy to think it'll get past Cruz and Trump delegates,” says Doug Sachtleben, communications director for the Club for Growth. “If neither gets to 1,237 before the convention, then the final choice should come down to those two."

Cruz has been warning against a brokered convention for some time. The Texas senator doesn’t even think Kasich should be considered, arguing he will have only won a single state. Cruz is pushing for the 2012 rule that required the eventual nominee to have won the majority of delegates in at least eight states to remain in place for 2016.

“This fevered pipe dream of Washington, that at the convention they will parachute in some white knight who will save the Washington establishment, it is nothing less than a pipe dream,” Cruz told reporters before a campaign stop in Wisconsin on Monday. “It ain’t gonna happen. If it did, the people would quite rightly revolt.”

Supporters of Kasich believe the Ohio governor would be more electable in November and would offer shelter for Republicans reluctant to support Cruz. For his part, Cruz has been pitching himself as a uniter of the GOP, touting endorsements, however tepid, from the likes of Mitt Romney and Jeb Bush. Some strategists believe this effort by Cruz, along with his ability to beat Trump in several states this primary season, will help quell concerns about his nomination. What’s more, Cruz has proven to be something of a master delegate hunter, which will help him in an open convention scenario.

There isn’t necessarily a groundswell of support for another candidate to emerge. But the continued floating of someone like Ryan underscores the idea that some in the party don’t like any of their options. Sen. Lindsay Graham, who has endorsed Cruz, once described, now famously, the choice between Trump and the Texas senator as akin to being shot or poisoned. But the nomination of another candidate altogether “means death by drowning,” Ornstein says.

While Ryan has largely remained above the fray, choosing to focus more on setting the party’s policy agenda and passing a budget, he has weighed in at certain points of turmoil. Last month, he gave a speech on the state of American politics. Sources close to Ryan say this speech and others are part of a broader vision he has been developing since becoming speaker. His efforts, they say, are bigger than Trump or this presidential race, and are geared toward a belief that the party is severely damaged and will likely remain broken even after the election in November.

Any attempt to nominate Ryan risks throwing the party further into flux. “For the nomination scenario to be realized, he'd have to resign as speaker, which would only introduce an entire new level of chaos to the party,” says Kevin Madden, a Republican strategist and former adviser to Romney’s presidential campaign. “It's also impossible to see the Cruz or Kasich forces, which are fully invested efforts focused on the presidential nomination with delegates in hand, allowing an outsider to prevail.”

Additionally, GOP strategists say that even if Ryan wanted to be drafted to the nomination, it would be harmful to his own brand and political aspirations down the line.

“Grassroots conservatives and Republicans are saying, ‘We want a time-out from Washington elected officials,’” says Mueller, the GOP strategist. “And to suggest that now we're going to have people in Washington hand-pick somebody, I don’t think is good for the brand Paul Ryan is trying to build … it doesn't help him as speaker or down the road.”

The only conceivable way forward for a Ryan nomination is if delegates came together organically to support him, Mueller says. But that still isn’t likely, given the careful orchestration of delegates already under way by the other campaigns preparing for an open convention. What’s more, neither Trump nor Cruz would cede to another candidate, especially Ryan.

Ryan “is viewed by a substantial number of Cruz as well as Trump delegates as a pillar of the establishment,” says Ornstein. “And up to this point, nearly every single survey, going back to the summer, of Republicans of all stripes shows 60 to 70 percent chose outsiders or insurgents.”

Of course, this political cycle has been marked by twists and turns that have defied what many knew to be true of presidential campaigns. But Ryan, for his part, remains determined not to take part.

“I do believe people put my name in this thing, and I say get my name out of that,” he told Hewitt. “If you want to be president, you should go run for president. And that’s just the way I see it.”