People close to Ryan continue to insist publicly that he has no interest in the nomination. And one associate of the speaker said he "guarantees" there has been no conversation with Charles Koch about the possibility, “because Paul has not had any conversation about it. He won't engage any conversation about it."

"Let me be clear, we never have advocated for a specific candidate in a presidential primary, and we have no plans to do so now,” Holden said.

One source close to Ryan said he would only be interested in it if the party could unite behind him, a scenario he can't envision. “I don’t know what to tell you? He doesn’t want the nomination. And can you imagine the backlash from the Trump forces if someone who didn’t run for president wins the nomination? It would be complete chaos," he said.

Koch believes Ryan would be a “shoo-in” at a contested convention, should the campaign get to that point. Though Koch's wealth gives him significant influence within the Republican Party, it does not necessarily translate into skill in political prognostication. Still, he and his brother David are fond of Ryan. As a source close to the brothers told The Huffington Post, they appreciate the agenda he has pursued as speaker, including opposition to tax extenders and heightened warnings against corporate welfare -- positions that contrast with the admittedly vague portfolio pushed by Donald Trump.

Charles Koch is confident House Speaker Paul Ryan could emerge from the Republican National Convention as the party’s nominee if Donald Trump comes up at least 100 delegates shy, he has told friends privately.

Despite the repeated denials of interest, speculation about an 11th hour Ryan nomination has only grown louder. Part of it is nervous chatter from Republicans over the prospect of Trump or Sen. Ted Cruz (R-Texas) being the party nominee.

But part of it is driven by Ryan's own history and by perceptions of politicians in general. It would be strange indeed if the same man who was the Republican nominee for vice president in 2012 -- typically the position that is a springboard to the nomination for president -- would not accept a shot at the top job. That is especially true considering the weak position in which Democrats find themselves. Hillary Clinton, the party’s likely nominee, has staggeringly high unfavorability numbers, which are only masked by Trump's even higher unfavorability with everybody other than older white men.

On Monday morning, Mike Allen, writing in Politico’s Playbook, quoted unnamed establishment Republicans talking up Ryan’s chance of claiming the nomination. And in a column Sunday, Republican strategist Alex Castellanos backed off his earlier prediction that Trump had the thing locked down, and used the same figure of 100 votes that Koch has used privately.

[I]f Mr. Trump is one hundred or more votes away from the nomination, it is unlikely he can find the delegates to get the ball in the end zone on the first ballot. He will turn the ball over on downs though nearly at the goal line. (OK, no more sports metaphors.) On the second ballot, he drops 200 or 300 votes or more and starts bleeding. Ultimately, he bleeds to death on the convention floor -- which you think would be good news for the candidate in second place, Senator Ted Cruz, unless, of course, you’ve met Senator Ted Cruz.

Cruz, Castellanos argues, is only attractive as an alternative to Trump, and as Trump fades, so does Cruz’s rationale. As attention moves to John Kasich, he adds, the question changes:

If GOP delegates start looking for an alternative to both Trump and Senator Cruz, why settle for Miss Ohio when you could marry Miss America? Why not wipe the slate clean and go for what delegates really want, the Republican Speaker? Former Vice-Presidential candidate Paul Ryan is a larger political figure. He has national experience and appeal. The Speaker has also managed to bring together unruly Republicans in the House, the Capitol's hotbed of insurrection. Most importantly, he is a fresher face, a new and more promising generation of Republican. He would have a better shot at uniting the Republican Party.

A Ryan associate dismissed the convention scenarios as conspiratorial folly spread by people who've watched too much TV drama. "This is where 'House of Cards' has totally changed things," said the associate. Ryan "views himself as a check on the madness. As this Rock of Gibraltar during the chaos. And if he suddenly becomes part of the circus, it is hard for him to play that role." (It’s unclear whether Charles Koch watches "House of Cards.")

To that point, there are many serious hurdles that would need to be cleared in order for Ryan to even be in the realm of consideration for the Republican nomination. First and foremost, Trump would have to end up with roughly 1,137 delegates -- or 100 short of the necessary 1,237.

The second hurdle is the rules. Under current bylaws, for a candidate to be nominated, he or she must have a majority of the delegate votes in each of at least eight states. That rule, 40(b), can be changed: The Rules Committee would have to suggest an alteration or amendment and then a majority of the delegates who vote at the convention would have to affirm it. But Cruz's campaign has moved deftly to put allies on the Rules Committee. And it is hard to imagine that both he and Trump would not instruct their delegates (which will very likely constitute a majority when combined) to defeat any effort to undo Rule 40(b), since maintaining the eight-state threshold would limit the potential nominees to just themselves.

"The easiest way for someone like a Paul Ryan is you have to change the rules to allow nominations from the floor, which means you have to eliminate 40(b), and put in a line in there that nominations would be accepted from the floor," said a Republican source involved in managing the convention process for the party.

The source went on to acknowledged that Rule 40(b) could be challenged after the first ballot -- as in, if no one wins in the first round of voting, an argument would be made that the eight-state threshold no longer applied. But even doing that would risk tremendous backlash from the very fervent supporters of Trump and Cruz.

"It's an extremely difficult proposition. Not impossible. But extremely difficult," the source said. Asked what would happen if it succeeded, the source replied: "Days of rage."

Conservative radio personality Hugh Hewitt asked Ryan about the convention rules during an interview in Israel on Monday. “You are going to be chairman, and there is quite a lot of talk about Rule 40(b). Do you think the rules of the 2012 Convention ought to bind this convention, Mr. Speaker?”

“You know, I don’t know, that’s not my decision,” Ryan said. “That is going to be up to the delegates. I’m going to be an honest broker, and make sure that the convention follows the rules as the delegates make the rules. As you probably know, the Rules Committee meets the week before the convention. I believe it’s two delegates from each state and territory, about 112 people who’ll set the rules, and I’m not going to make an opinion or a judgment one way or the other, because it’s their decision, the delegates’ decision, who are the grassroots of the party, by the way. It should not be our decision as leaders. It is the delegates’ decision. So I’m not going to comment on what these rules look like or not. But I do believe people put my name in this thing, and I say get my name out of that. This is -- if you want to be president, you should go run for president. And that’s just the way I see it.”

UPDATE: An astute reader notes that the Koch brothers have a history of pushing Ryan for the White House. As the New Yorker's Jane Mayer reported in her book, Dark Money, Sean Noble, a Republican consultant often referred to as a "Koch operative," tried "for months" to persuade Ryan to run for president in 2012. And he did so with the assent of the Kochs.

"The billionaire backers were eager for him to apply his ‘sharp knives’ to the federal budget," Mayer wrote. "But Ryan had demurred. Neither he nor his wife relished a presidential marathon. ‘Wouldn’t it be easier just to be picked as vice president?’ he asked an emissary from the Kochs, in a meeting in the congressman’s Washington office. ‘Because then it’s only, like, two months.’"

Ryan ended up getting his wish: He was selected by Romney to be the vice presidential nominee, only to be stuck on a losing ticket.

Matt Fuller contributed reporting.

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