May's pitch is more than just an environmental one: She's arguing that denying Trudeau or Conservative Leader Andrew Scheer a majority government would spur better government in Ottawa, giving Canada a better shot at meeting and even exceeding its emission goals and addressing social issues. She says that a minority Parliament — one where parties are forced to form coalitions on every issue, and where members are more likely to collaborate across party lines — with a small-but-influential caucus of Green members could push the other parties to pass stronger climate legislation than the Trudeau government has, if they want to prevent the government from falling.

The party isn’t expected to move beyond the single digits in its number of MPs. But May is betting Canadian voters are frustrated enough with the status quo parties — and are more concerned than ever before about the future of the planet — to cast their ballots elsewhere. Climate change and the environment writ large are major issues for B.C. voters, particularly in the Vancouver area. Indeed, Greens and their rivals, the New Democratic Party, alike point to the Trudeau government’s endorsement of the Trans Mountain expansion on the stump as a prime example of the sitting government’s contradictory stances on climate.

Voters who have cast their lot with Canada’s establishment parties — the Conservatives, the Liberals or the NDP — “are no longer happy with the choices they’ve made, and they’re looking around,” May said over a cheese and lemonade spread at her husband's house in Vancouver's tony Kitsilano neighborhood.

But the question remains whether concerns about climate change and frustration with mainstream political parties are pressing enough to spur voters into the Greens’ embrace — and to convince them a “strategic” vote for Liberals to prevent Scheer from becoming prime minister is a false premise.

“The task [May] has is getting people to go from feeling good about her — liking the idea of a Green Party and agreeing with them on a lot of important issues — with converting that into an actual vote,” said David Coletto, CEO of Abacus Data, POLITICO’s Canadian polling partner. “And that has always been their Achilles heel.”

LIVE ANALYSIS: Follow POLITICO reporters' latest analysis as Canadian leaders meet in the 2019 Federal Leaders’ Debate, starting tonight at 6:30 p.m. | POLITICO illustration/AP

As if to underscore her rejection of traditional party politics, May even campaigned with a party rival Sept. 18, when the Greens’ leader made an off-schedule pit stop during one of her visits here — to speak at a rally for independent candidate Jody Wilson-Raybould, the former Liberal Cabinet member whom Trudeau expelled from his caucus in the aftermath of an ethics scandal that smudged his reputation.

“If this isn’t doing politics differently, I don’t know what is,” May said that night at a Vancouver Hellenic center in Wilson-Raybould’s riding of Vancouver Granville, where the Greens are also fielding a candidate. May named the "excessive, antidemocratic power of the well-organized big three parties with their backrooms dictating to members of Parliament what they can and can’t do" as a trend she's seen grow over the last eight years since she's served as an MP for the Saanich-Gulf Islands riding on Vancouver Island.

“MPs have lost their individual voices,” said Paul Manly, the second Green candidate elected federally in Canada who represents Nanaimo-Ladysmith on Vancouver Island. “They’ve lost the ability to represent their constituents properly because they’re not representing their constituents to Ottawa — they’re representing their leaders and the party to their constituents.”

Trudeau has fashioned himself a climate champion as American influence on the issue has evaporated, and his embrace of a carbon tax may ultimately shield him on the issue. Nationally, his Liberals are campaigning on climate policy by juxtaposing their record over the past four years with that of the Conservatives, obliquely equating the right-leaning party with President Donald Trump by claiming they want to “make pollution free again.” Meanwhile, the NDP is training its counternarrative at the Liberals. “You. Bought. A. Pipeline,” read one email the party sent Sept. 24 after Trudeau vowed to make Canada a net-zero carbon emitter by 2050.

That leaves the Greens, who say none of the major parties has put forward a sufficient plan to stave off the worst effects of global warming.

“The human toll now of the climate emergency is impacting every part of Canada,” May said, pointing to historic floods in Quebec and New Brunswick and severe forest fires in British Columbia. “This is not a future threat. This is a clear and present danger, and there isn’t any place in Canada where people aren’t concerned.”

Canadian voters rank climate change as a major electoral issue, according to Abacus/POLITICO polling released Sept. 23. Still, citizens are far from united around specific policy approaches, and Coletto said global warming “doesn’t feel that it’s the defining issue of this campaign” — not that any such issue has emerged.

Besides selling voters on a climate plan billed as superior to the Liberal or NDP offerings, the Green Party also faces a tall order in convincing them that a vote for the Greens is, in Manly’s words, “viable.”

The Greens are banking on recent provincial wins — including attaining official opposition status in Prince Edward Island and picking up seats in the New Brunswick Legislature — to propel them federally and inch them closer to formal party recognition in Parliament, which is 12 members.

Coletto said he doesn’t expect the Greens to win more than five or six seats nationwide — an outcome that still would represent a historical moment for the party.

While the party’s history of representation in the provincial B.C. government, coupled with May’s and Manly’s presence in Ottawa, bode well for Greens to pick up seats in the Vancouver area, Coletto said, the challenge will be expanding that momentum into other regions of Canada and to ridings where the competition is focused around the mainstream parties.

“There’s no Green wave that is sort of carrying them forward,” he said.

Still, Coletto said, there’s potential for May’s party to break through further, such as during Monday's English-language debate in Ottawa. May, Trudeau, Scheer, New Democratic Party Leader Jagmeet Singh, People’s Party of Canada Leader Maxime Bernier and Bloc Québécois Leader Yves-François Blanchet will face off for two hours to make their cases to Canadians.

An opportunity like the debate “is her best shot at connecting and trying to create that wave,” Coletto said, pointing to the Greens’ meager campaign spending history compared to the other parties.

One NDP candidate, Bob Chamberlin, suggested Manly’s win earlier this year in the by-election in Nanaimo-Ladysmith was in part a fluke thanks to low voter turnout for a contest just months from the general election. Still, he also acknowledged voters wanted to “send a message” to his party about the environment.

Manly said the B.C. NDP’s support for a liquefied natural gas export facility in Kitimat — and Singh’s silence about the project — has turned off voters there.

“I think a lot of people who are concerned about climate change just see this as doublespeak,” he said. “You’re talking a good game, but you’re not following through.”

The message Chamberlin said in an interview he’s hearing this time around from constituents who cast a “protest vote” for Manly in May is that they’re “now back with the NDP for the general election.”

That element of the Green Party’s identity — the “protest” vote that sends a message to politicians about working differently, even beyond climate change — could help them at the polls if Canadian attitudes around the mainstream parties deteriorate, Coletto said.

“I don’t think that’s where Canadians really are right now, but there’s an element of them being kind of like a protest vote that’s not just about climate change or the environment,” he said.

The campaign isn’t solely Greens versus NDP; some Greens are eyeing Liberal candidates as their primary competition.

Take Jesse Brown, who’s running in Vancouver Centre to unseat Liberal Hedy Fry, the longest-serving female MP in the country’s history who also happened to beat a sitting prime minister — Progressive Conservative Kim Campbell — in 1993.

While Fry’s riding is rated as “safe” for Liberals by prominent Canadian professor P.J. Fournier, Brown said he’s vying for the seat to register constituents’ displeasure with the Liberals’ embrace of the Trans Mountain Pipeline project.

“At every possible moment where it’s head-on-head with Hedy Fry, I’m going to be bringing up this horrible decision to essentially throw away any of their Paris climate agreement targets,” he said over tea late last month near his downtown office.

Fry expressed dismay in 2016 when Trudeau first determined the pipeline project was in the national interest, saying the decision would cause her “problems” in the 2019 election.

Now, Fry says her constituents have largely “moved away from being very, very anti-TMX” as Liberals have unveiled more climate-focused policies. Those voters, she said, are treating their votes strategically to hedge against a government led by Scheer.

“Democracy’s always about strategic voting, and if you’re going to do a protest vote just because it makes you feel good, you may end up with a Conservative government,” she told POLITICO.

May and her candidates are hitting back at that notion. A minority government is the ideal governing situation, she said, because it prevents the concentration of power within one party that can then break election promises with no consequence before the next election.

That’s not to say Greens would be malleable on climate policy, should other parties seek to form a coalition with them after Oct. 21.

Party MPs would only provide votes of confidence in a government that would make a “verifiable” commitment to meet Greens’ climate benchmarks, May said. Benchmarks include cutting greenhouse gas emissions 60 percent below 2005 levels by 2030, with Canada becoming a net-zero polluter by 2050.

“None of them are close,” May said. “There’s better lip service, depending on the party, but … we don’t work with anybody who isn’t prepared to ensure our survival. We’d bring down the government the first vote, we’d go back to the polls.”

That leverage, she said, will “terrify” the other parties.

Polling suggests Greens’ support nationally is more than double where it was during the last election during 2015, Coletto said, with around 40 percent of Canadians saying they’re “open” to voting for the party's candidates.

May has two more weeks to try to sway those voters.

“There’s lots of potential there,” he said. “But the challenge is always for smaller parties in our system is … the impetus is to vote strategically.”