Libertarian Party presidential nominee Gary Johnson is making surprising inroads among Hispanic and younger voters — two planks of the Obama coalition that Democratic candidate Hillary Clinton has been banking on to help carry her to victory.

Those voters could play an outsize role in the West. Mr. Johnson has been building support in Colorado and Nevada, two swing states where Mrs. Clinton and Republican presidential nominee Donald Trump have tried to attract Hispanics.

“This race in the Hispanic community — if Gary Johnson launches a very aggressive effort, he has the ability of [not] necessarily coming in second, but very closely beating Hillary if they dedicate enough resources,” said Rafael Fantauzzi, co-chairman of the recently formed Tercera Opcion PAC, a pro-Johnson outside group.

Mr. Trump has spent the past week trying to calibrate his immigration stance, hoping to appeal to Hispanic voters without losing support of conservatives who support a crackdown on illegal immigration.

Democrats say Mr. Trump’s history as a hard-liner on immigration will haunt him.

Mr. Johnson supports President Obama’s deportation amnesty, which plays well in Hispanic communities, and his support for criminal justice reform could attract younger Hispanic voters, Mr. Fantauzzi said.

“In the past few years, you’ve seen a 400 percent increase in the number of Hispanic women that have been incarcerated, mostly for possession of marijuana,” Mr. Fantauzzi said. “Among younger voters, it’s a huge issue.”

Mr. Johnson is fighting to cross the relevancy threshold in the presidential race. If he can earn 15 percent support in a series of polls, he will be allowed onto the national stage for prime-time debates.

In states such as Colorado, Mr. Johnson has hit that 15 percent mark. But in national polls, which matter more now, his numbers are hovering just below 10 percent. He is, however, outperforming among Hispanics, according to some of those surveys.

A Fox News poll of Hispanics showed Mrs. Clinton with 59 percent support in a three-way contest. Mr. Johnson was effectively tied with Mr. Trump, with 16 percent to the Republican nominee’s 17 percent. In May, Mrs. Clinton was at 58 percent, Mr. Trump was at 21 percent and Mr. Johnson was at 9 percent.

Mr. Trump has pledged repeatedly to build a wall along the U.S.-Mexico border, but he has been on the defensive in recent days over his plans on what to do with the approximately 11 million illegal immigrants in the U.S.

The Republican’s team insists his stance has not changed, but a policy speech scheduled for Thursday in Colorado has been postponed as the candidate receives additional counsel.

Daniel Garza, executive director of the Libre Initiative, a conservative Hispanic advocacy group with ties to the Koch brothers, said distaste for the two major-party nominees has left his group in a “holding pattern,” providing an opening for Mr. Johnson.

“Gary Johnson, clearly, I think, has a good message on stopping the waste of taxpayer money, unleashing economic growth and preventing American bankruptcy, and those are important issues,” Mr. Garza said. “There is no question that he is up for consideration by a lot of Latinos.”

Mr. Johnson’s sweet spot appears to be younger voters, Hispanic and otherwise.

He led outright among voters younger than 25 in a recent Investor’s Business Daily poll, receiving 35 percent support to Mrs. Clinton’s 30 percent, Green Party nominee Jill Stein’s 14 percent and Mr. Trump’s 12 percent.

Mr. Johnson was a close second to Mrs. Clinton among voters younger than 35 in a Quinnipiac poll on Colorado, winning 29 percent support to her 34 percent. Overall, he was at 16 percent in the poll — one of his best showings in any state or national poll thus far in the race.

Nicholas Sarwark, who chairs the Libertarian National Committee, says data show Mr. Johnson is pulling more support from Mrs. Clinton than he is from Mr. Trump. Many of those voters have written off any kind of consideration for the Republican nominee, he said.

“There are a lot of voters where the question they’re asking themselves right now is: Johnson or the Democrat? They didn’t consider the Republican,” Mr. Sarwark said. “That would be like someone [says] your dinner choices are chicken, fish or dirt. Dirt’s just not on the menu.”

Mr. Johnson and running mate Bill Weld, a former Massachusetts governor, have started to engage with Hispanic media and recently participated in a forum with Fusion’s Jorge Ramos.

Asked about flipping the ticket to make Mr. Weld the presidential candidate, which many Republicans have suggested, Mr. Weld said at the forum that he hears that from East Coast people who have known him for many years and that Mr. Johnson is the one with the cachet out West.

“When I go out West with Gary, it’s, ‘Hey, Gary, who’s this weirdo you have with you? He doesn’t seem to speak Western,’” Mr. Weld said.

After largely relying on media hits to deliver his message, Mr. Johnson has campaigned in Las Vegas and his home state of New Mexico.

Ted Jelen, a political science professor at the University of Nevada, Las Vegas, said the large number of undecided voters in a close presidential race in the state leaves an opening for Mr. Johnson.

“The libertarian label has a very positive connotation in a lot of Nevada,” Mr. Jelen said, particularly outside of Clark County and the surrounding Las Vegas area. “I could see Johnson getting into double digits.”

Polling also has shown Mr. Johnson running relatively strong in Utah. The campaign’s home base is in Salt Lake City, and Utah is demographically one of the youngest states in the country.

Mr. Garza said an outright win might be tough for Mr. Johnson, but he sees potential for the Libertarian to disrupt the race in enough Western states to deny any one candidate 270 Electoral College votes and throw the decision to the U.S. House.

“If you can peel away Nevada or Utah or some other state where you can dig in and make your case, you put it into the hands of Congress, and [then] you come in as the one who was the consensus ticket or whatever, and you’ve got a shot. You’ve got a legitimate shot,” he said.

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