A top Koch Industries official also said the story was inaccurate.

“Reports that David Koch has pledged his support to Gary Johnson – or any candidate running for president for that matter – are untrue," Philip Ellender, president of public affairs at Koch Companies Public Sector, said in a statement.

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The rumor began with a story by a freelance contributor to the Daily Caller, which cited "a source within Johnson's campaign" to claim that Koch would spend "tens of millions of dollars" to help Johnson if he won the Libertarian Party's nomination next weekend in Orlando. A non-denial by "a source close to David Koch" powered the rest of the story, as Johnson's small organization generally dodged the question.

Were Koch to invest in the Libertarian Party, at all, it would represent a major break from 2012 -- when he served as a Republican delegate for Mitt Romney -- and a flashback to an awkward past. In 1980, Koch joined the Libertarian Party and spent $2 million to boost the party as its candidate for vice president. The result was the best showing in the party's history, with 1.06 percent of the popular vote. (In 2012, Johnson became the first Libertarian to crack 1 million votes, representing 0.99 percent of the electorate.) In the aftermath, Koch and allies like Cato Institute founder Ed Crane were effectively chased out of the party by a "paleo" wing that worried about the party being watered down.

"Koch explicitly wants to run the movement like a corporation," wrote Murray Rothbard, a paleolibertarian thinker and activist, according to Brian Doherty's movement history "Radicals for Capitalism." To Rothbard, Koch represented the party "sliding down the slippery slope to opportunism and sellout of libertarian principle," and by 1984, that faction was defeated.

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David Koch, and his brother Charles, turned their energy and donations over to libertarian think tanks, reengaging in electoral politics during President Obama's term. Some of the divisions inside the libertarian movement were smoothed over as Koch funding helped elect conservative Republicans and as Sen. Rand Paul (R-Ky.) attempted to build bridges between his father's "liberty movement" and the Kochs by appearing at their donor summits.

Still, Johnson's campaign is in no position to confirm that Koch would spend more than any third party has ever received to help a Johnson-led ticket. "It sounds like someone who wants to be a player said something he couldn't know," suggested John Vaught LaBeaume, a Johnson spokesman. Johnson, who announced this week that former Massachusetts governor William Weld would serve as his running mate if nominated, wouldn't comment on how the Koch rumor would play.

"I couldn't say either way whether it affects the delegates in Orlando," he said.

Last month, the Federal Elections Commission reported that Johnson's 2012 campaign remains $332,191 in debt.