Libertarian Party leaders are convinced that 2016 will be a breakout year, with an insurgent spirit coursing through the electorate and voters looking for an alternative to strikingly unpopular candidates from both major parties.

As he prepared for the party convention over Labor Day weekend in Orlando, Florida, presumptive Libertarian presidential nominee Gary Johnson said that all of the pieces are falling into place for his party to have a dramatic impact in November.

The former New Mexico governor has been polling in double digits in theoretical three-way contests against likely Democratic nominee Hillary Clinton and presumptive Republican nominee Donald Trump.

The party also is experiencing a surge of new members. And widespread dissatisfaction with the status quo in Washington has spurred political movements that are challenging both the GOP and Democratic Party establishment.

If Mr. Johnson garners 10 percent of the vote in November, it would be Libertarians’ strongest showing since the party began fielding presidential nominees in 1972.

Libertarian National Committee Chairman Nicholas Sarwark said he expected a “breakout year” regardless of which of the 18 candidates captures the presidential nomination next weekend.

“What this election is showing people is that the conventional wisdom in politics is out the window. We will be the only alternative on all 50 state ballots to the bullies being nominated by the two old parties,” he told The Washington Times.

Mr. Johnson, who last week announced Massachusetts’ former Republican Gov. William Weld would be his running mate, is expected to easily win the nomination and boasted that it would be the party’s “strongest ticket ever.”

“With two of the most polarizing figures in U.S. politics as the likely major party nominees, the Libertarian Party has more opportunities than ever before,” Mr. Johnson, who captured the Libertarian nomination in 2012, said in a recent interview with Newsmax’s John Gizzi.

The most significant competition for the nomination is expected to come from Austin Petersen, owner of LibertarianRepublic.com.

The Libertarian Party so far this year conducted four non-binding primaries and caucuses. But the party’s nominee will be elected directly by registered delegates at the convention that opens Thursday at Rosen Centre Hotel and Resort in Orlando.

Mr. Johnson has argued that Mr. Trump’s presence in the race would benefit the Libertarian ticket, but polls indicate Mr. Johnson’s run hurt Mrs. Clinton as much as the billionaire businessman.

A recent Fox News poll of a three-way race the included Mr. Johnson showed him taking 10 percent of a theoretical general election vote, but that barely altered the outcome of the race.

With Mr. Johnson in the mix, Mr. Trump edged out Mrs. Clinton 42 percent to 39 percent. Without Mr. Johnson, Mr. Trump still beat the former secretary of state 45 percent to 42 percent, according to the poll.

Mr. Johnson had roughly the same effect on both major party candidates.

A Monmouth University poll in March showed a similar outcome, with Mr. Johnson taking 11 percent of the vote but not significantly altering the outcome.

In that hypothetical three-way contest, Mrs. Clinton garnered 42 percent of the vote — down 6 points from the two-person race — and Mr. Trump got 34 percent — down 4 points from the two-person race.

Still, Mr. Johnson said that he is ready to go after Mrs. Clinton and Mr. Trump for their big-government agendas.

Mr. Johnson said that Mr. Trump’s big-government thinking was evident in his plans to tackle illegal immigration, which is the cornerstone of the billionaire businessman’s campaign.

“He says he wants to build a wall and then deport 11 million people here illegally,” Mr. Johnson said. “That’s big government right there. These are people who take jobs Americans don’t want and whose only major barrier is the language, which they can overcome.”

He said Mrs. Clinton would “do more to make government grow and isn’t going to change anything. At the end of the day, taxes will go up.”

Republican National Committee spokesman Sean Spicer dismissed the idea that Mr. Johnson would hurt Mr. Trump’s chances of winning the White House.

He said he has “zero” concern about Mr. Johnson, who appeared to lack the campaign or organization needed to have a big influence on the election.

“I think the media frankly wants a third-party. They want a fight,” Mr. Spicer said. “They are not going to get it.”

Mr. Spicer said there are clear signs that the GOP is consolidating behind Mr. Trump and said Democrats should be concerned that Mrs. Clinton has struggled to woo supporters of Bernard Sanders, pointing to a recent poll that showed some of the Vermont senator’s backers are planning to back Mr. Trump in the general election.

“So I appreciate the intrigue about the Republican Party, [but] I think the Democrats have a much, much, more substantial problem that is really bearing out in the polls,” he said.

⦁ Seth McLaughlin contributed to this report.

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