Libertarian candidate for president Gary Johnson speaks at a rally outside the New Hampshire State House in Concord, N.H., this week. (Libby March/For The Washington Post)

On Friday morning, the third day in his four-day New England campaign swing, Libertarian presidential nominee Gary Johnson told a joke. He was the punch line.

“This is a crazy election,” Johnson said, looking out at dozens of Mainers who had come out for a breakfast meet-and-greet. “You know how crazy this election is? I’m going to be the next president of the United States. That’s how crazy!”

Johnson, a two-term governor of New Mexico, has avoided the fringe label that often sticks to third-party candidates. Since announcing former Massachusetts governor William Weld as his running mate, Johnson has risen in the polls to the high single digits — and to the mid-teens in some swing states. His rallies draw hundreds of voters, bigger than anything he saw during his 2012 bid. He talks about “spoiling the party,” and voters cheer.

Despite that, Johnson is struggling to grab the prize he has eyed all year: to be invited to the televised presidential debates. He needs to close in on 15 percent in an average of polls, and he is doing what he can. Two super PACs are trying to boost him in. It’s not clear that they can pull it off.

[Trump and advisers remain split on how far to move toward the middle]

Recent U.S. politics has favored candidates from the Democrat and Republican parties, but here are seven examples of candidates who ran under a different mantle. (Sarah Parnass/The Washington Post)

The support Johnson has so far is easily explained; in a year of not one, but two historically unpopular major-party candidates, voters are looking for an alternative to Democrat Hillary Clinton and Republican Donald Trump. Johnson may hold particular appeal for Republicans trying to protect their majorities in Congress; he gives voters an alternative to Trump at the top of the ticket yet allows them to return to the GOP lineup down the ballot.

Relentlessly positive, bounding from event to event in black Nikes and Carhartt jeans, Johnson approaches the debate problem by talking like he has solved it. In 2012, he briefly ran as a Republican — the party he was part of in Santa Fe — and was yanked offstage after a first, flailing debate performance.

“I had 60 seconds to make my pitch, and in the 60 seconds, I was being interrupted,” Johnson said in an interview here. “Now, I can say the same thing — and I’ve got three minutes. Uninterrupted! Three people onstage, audience bigger than the Super Bowl. I don’t think they’d get away with cutting me.”

They might. The Commission on Presidential Debates, which has controlled the process since 1988, has held fast to its 15 percent threshold. A Johnson-backed lawsuit against that threshold was thrown out this month, however, and the voters filing into Johnson-Weld rallies last week were acutely aware that their man might be kept offstage.

[Inside debate prep: Clinton’s careful case vs. Trump’s ‘WrestleMania’]

“I’m not for either of the choices­ we have right now,” said Roy Hermann, 65, who caucused for Bernie Sanders but showed up in Portland to hear Johnson. “I’m not even sure if I’ll vote for this guy, but I have a great deal of respect for him.”

The day before, at a Johnson-Weld rally in Concord, N.H., 14-year-old Aubrey Pelletier hoisted a sign that read “15%!” Her father, Brad, 39, worried that too many voters limit the news they read and couldn’t see the point of choosing Johnson.

Alexis and Eli Luicha stand close shelter under an umbrella during Johnson’s rally in Concord. The Luichas are independent voters from nearby Andover, N.H. (Libby March/For The Washington Post)

“People are afraid of wasting their votes,” he surmised. “On Facebook, I see Gary Johnson stuff all the time. When I talk to people, they know who he is now.”

As Johnson and Weld stumped across New England, they were recognized by voters — something new in the past three weeks, they said. Fundraising, according to the campaign, has surged in the same period.

Neither Republicans nor Democrats know which nominee that helps. The polls that show Johnson at or above 10 percent have Clinton’s lead growing if he is removed as a choice — but she has got a lead either way. At rallies in New Hampshire and Maine, voters with Bernie Sanders T-shirts stood near people wearing the “Hillary for Prison” shirts sold by far-right radio host Alex Jones. Some cheer when Johnson calls for ending corporate taxes; some cheer when he insists that “black lives matter.” All cheer when he endorses ballot measures to legalize marijuana.

Asked whether he would encourage his voters to pick Republicans or Democrats when they went down their ballot, Johnson demurred. “The wonderful thing about being a Libertarian is that you don’t have to tell anybody to do anything,” he said.

[New Trump campaign chief faces scrutiny over voter registration, anti-Semitism]

Two libertarian efforts are underway to boost Johnson past the debate commission’s 15-percent hurdle. Purple PAC, steered by former Cato Institute president Ed Crane, began a $1 million ad buy last week, with cable spots casting Johnson as an “honorable choice” who favors tolerance and free markets.

“They’re not as ideological as I would probably prefer,” Crane said of Johnson and Weld. “But on the broad issues of social tolerance, restraint in foreign policy, markets over crony capitalism, they’re very good.”

Alternative PAC, launched by former FreedomWorks president Matt Kibbe, is spending $50,000 to kick-start a Web campaign aimed at millennials. One ad, “Balanced Rebellion,” stars an Abraham Lincoln impersonator who promises that Johnson won’t “send you to fight wars overseas” or “tell you who to marry.”

“It’s like a two-horse race where one horse cheats and the other one eats Muslims,” the Lincoln actor says of the Clinton-Trump race.

The spot was designed by Harmon Brothers, the firm behind a viral ad in which unicorns defecate rainbow ice cream to promote a toilet aid.

Johnson is more tactful. In his campaign speech, an optimistic spiel on how free markets (“Uber everything”) and active citizens can fix the country, he tells one joke about Trump. The Republican nominee, he said, watched the Olympics to see “how high those Mexican pole vaulters could go.” Neither Johnson nor Weld is inclined to attack Clinton, something they have been trying to correct.

“You make mistakes along the trail,” Johnson said in Concord, referring to a CNN town hall — one of his highest-profile events — where he declined to criticize Clinton. “If I had to do that over again, I’d have said: She’s beholden.”

“I’ve made a mini-career of defending Mrs. Clinton on the use of the private server,” said Weld, who added that newer revelations about her email gave him pause.

That light tone has become central to the Johnson-Weld campaign. The two standard-bearers for libertarianism have become some of the least ideological candidates in America.

On the stump, Weld describes the Libertarian Party as “a six-lane highway going right up the middle between the two parties,” and Johnson talks about what can be achieved when partisans cross the aisle.

That has led to steady criticism from more traditional libertarians, who pounce on every Johnson or Weld sop to the center as a gaffe. Weld, who signed a gun-control bill as governor, struggled to win the Libertarian vice-presidential nomination. Jason Sorens, the founder of the Free State Project that encourages libertarians to move to New Hampshire, said he had seen “some demobilization of the LP ticket’s natural base over guns.”

After Johnson refused to rule out a tax on carbon — only if it were revenue-neutral and it replaced income taxes — he was criticized by libertarians on social media.

Crane, Kibbe and other libertarians knew some of this was coming. The Republican primary campaign of Sen. Rand Paul (Ky.), designed to build on the support of father Ron Paul’s three ­libertarian-flavored presidential bids, made a bid for conservative voters that put the base to sleep.

“I’m still on the fence about whether I’m going to cast a write-in vote for ‘none of the above’ or myself,” said Darryl Perry, a New Hampshire voter who ran against Johnson for the Libertarian presidential nomination. “I know a few [people] who have said, ‘Well, he’s the lesser of the evils.’ The lesser evil is still evil in my eyes.”

But the dazzling possibility of the debate invite — something no Libertarian candidate has ever achieved — has kept most fellow travelers on board. Dan Fishman, the campaign’s 48-year-old New England director, has walked away from each rally with pages of new sign-ups. “It’s getting easier and easier to train people,” he said, crediting the NationBuilder software that had helped the Trump campaign convert its ­giant crowds into volunteers.

At one rally, in Concord, close to 300 people stood in a steady and meteorology-defying rain to hear Weld and Johnson speak about the six-lane highway between the parties.

“Standing in the rain,” Johnson said with disbelief. “You honor us. You really do.”