It’s easy to tell the Democrats and Republicans from the Libertarians these days. The Libertarians are the ones with the big grins on their faces.

The anti-establishment unrest rattling the two major parties has resulted in a landmark year for the Libertarian Party, which convenes its national nominating convention Friday in Orlando, Florida.

Fundraising and party membership have surged. Name recognition is up. The front-runner for the party’s presidential nod, former New Mexico Gov. Gary Johnson, is hitting double digits in some polls as voters dissatisfied with the presumptive Democrat and Republican nominees search for a third-party alternative.

“I will be the only third-party candidate on the ballot in all 50 states,” Mr. Johnson told The Associated Press. “I’m it.”

Indeed, despite talk of a third-party run by Republicans revolting against presumptive GOP nominee Donald Trump, no such candidacy has emerged. That would appear to leave the #NeverTrump Republicans nowhere to turn except to their small-government brethren in the Libertarian Party.

At the same time, the Libertarian ticket could also appeal to disappointed Democratic supporters of Sen. Bernard Sanders of Vermont, about 25 percent of whom have told pollsters they would not vote for Hillary Clinton if she were the nominee, as looks likely.

“If you’re looking to walk away from Donald Trump, it [the Libertarian Party] looks like the place to go,” said political analyst Floyd Ciruli. “But there are Libertarian aspects within the Sanders forces also, whether it’s personal liberty and smoking marijuana to the desire for radical change, which is probably as much as anything what Sanders stands for.”

He added that “both parties have factions that are likely to be unsatisfied with the nominees and are looking for some place else to park. So this could be one of those extraordinary years.”

Mr. Johnson has already reached out to the Sanders camp. “When it comes to economics, we come to a ‘T’ in the road. But on the social side of Bernie, I get it,” he told CNN.

The Libertarians raised their profile last week when former Massachusetts Gov. William Weld’s announced he will seek the party’s vice presidential nomination. He and Mr. Johnson, both former Republicans, have said that they want to run together on the national presidential ticket.

“I don’t think we’d be doing it if there weren’t this feeling in the country of disquietude with the two leading candidates, who are Mr. Trump and Mrs. Clinton, and that’s what makes us see the real political opportunity and that’s what makes me think the game is worth the candle,” Mr. Weld told MSNBC.

Mr. Johnson has released a rash of pre-convention videos in the last week, including one restating his commitment to smaller government.

“Look, government wastes your money because it’s too big and it tries to accomplish too much. The Department of Commerce. Why do we have one?” Mr. Johnson says. “Get the government out of the way. We don’t need a Department of Commerce. We need commerce.”

Delegates will vote separately on candidates for the presidential and vice presidential candidates during the Sunday nominating process. There are 18 candidates for the presidential nomination, but only those collecting at least 30 tokens from convention delegates will eligible to participate in the Saturday debate.

Other leading candidates for the presidential nod are FreedomWorks’s Austin Peterson, cybersecurity entrepreneur John McAfee and New Hampshire radio talk-show host Darryl Perry.

As the party’s nominee in 2012, Mr. Johnson received 1.27 million votes, or just under 1 percent of the total, the most in the Libertarian Party’s history. This year, however, polls suggest he could easily top that outcome.

Two polls released in the last week show Mr. Johnson capturing at least 10 percent of the vote versus Mrs. Clinton and Mr. Trump. A Morning Consult survey released Tuesday found Ms. Clinton leading with 38 percent, followed by Mr. Trump with 35 percent and Mr. Johnson with 11 percent, but with 17 percent of voters still undecided.

Ten percent is huge for a third-party candidate, but it’s not enough to qualify for nationally televised presidential debates. Under the rules, Mr. Johnson would need at least 15 percent in five national polls.

“Given that Trump and Clinton are sporting historically high negative ratings, Johnson’s polling makes a fair bit of sense,” said FiveThirtyEight’s Clare Malone. “Gary Johnson is neither Donald Trump nor Hillary Clinton. He might not win a state, but he could make some noise.”

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