The Libertarian Party’s key challenge is getting voters’ attention, and party officials see the general-election debates as crucial to that effort. Along with other third parties, the Libertarians have taken legal action to see the Commission on Presidential Debates change their qualifying criteria. Currently, per Commission rules, candidates must appear on enough state ballots “to have a mathematical chance of winning a majority vote in the Electoral College” and must get 15 percent of the vote in five national polls selected by the Commission.

Getting on state ballots might not be that difficult: National committee Executive Director Wes Benedict predicts the party will appear on 49 ballots this cycle, though it is aiming for all 50. But when it comes to polls, Johnson said, the party is in a catch-22. He explains the problem this way: Polling companies do not test libertarian candidates because mainstream media does not cover them much, and the mainstream media will not cover them much because they say, “‘You’re not polling.’” Of course, Johnson is not polling because “I’m not in the poll!” He did see some encouraging numbers in one late-March Monmouth University survey, in which he was the only Libertarian tested in a hypothetical contest with Hillary Clinton and Trump. Johnson got 11 percent of the vote. In the 2012 election, he received roughly 1 percent of the vote nationwide, a record for the party.

From the party’s perspective, the consequences of not debating are dire. “When people watch those debates, they think those are the candidates running,” Benedict said, “and others must not matter if they’re not in those televised debates.” The lack of polling and media coverage also makes it difficult to assess where the Libertarian candidates stand in the race. And the candidates themselves don’t even know how many delegates they will snag at the upcoming convention, because Libertarian delegates are uncommitted—or “squishy,” in Petersen’s words. Like Democratic superdelegates, they are not tied to any candidate.

The Libertarian candidates know they have high hurdles to vault, but they sense this cycle could be riper than usual for potential converts: Many voters are disenchanted with the Republicans and Democrats and want somewhere to turn. Even Johnson, who told me back in January that he had “no delusions of grandeur,” last week said yes when I asked if he was in the race to win the presidency. McAfee, known for his intense personality, took a harder line on his eventual victory: “I don’t have the time to waste on folly.”

The contenders are trying to draw major-party voters to their cause. Johnson and Petersen both made overtures to the anti-Trump crowd once Cruz dropped out of the race on Tuesday and Trump’s nomination looked near certain. Petersen, who bucks his party’s platform by identifying as pro-life, has specifically reached out to Cruz voters on social media.