TORONTO — Justin Trudeau started his term in 2015 by presenting a gender-balanced, multicultural Cabinet, which he said was a signal that his Liberal government would pursue policies of social equality at home, the “highest ethical standards” in government and Canadian leadership abroad.

Just 43, movie-star handsome and bearing one of the most famous names in the country’s politics, Mr. Trudeau sparked hopes at his inauguration that he would raise Ottawa’s clout and visibility around the world simply through the force of his personality.

Four years later, Cabinet resignations, a damaging ethics scandal, the grind of governing and battles with the provinces have dimmed Mr. Trudeau’s luster. Canada’s 23rd prime minister is now facing a tough battle for a second term in Oct. 21 elections.

“He started out by taking this high-toned, morally uplifting plan to lift hundreds of thousands of people out of poverty, a dedication to the environment, and especially a change towards women and aboriginals,” said Pat Gossage, founder of Media Profile and onetime press secretary to Mr. Trudeau’s father, former Prime Minister Pierre Trudeau. “That’s all backfired.”

Mr. Trudeau’s highest-ranking aboriginal Cabinet minister, Attorney General Jody Wilson-Raybould, resigned this year after accusing her boss of pressuring her to reduce criminal charges against the Montreal-based SNC-Lavalin, a politically connected global engineering firm that is one of the corporate crown jewels of Mr. Trudeau’s political base of Quebec. Though Ms. Wilson-Raybould and an official ethics inquiry found Mr. Trudeau broke no laws, the long-running investigation tarnished his political brand just as the election season was gearing up.

Confidence in Mr. Trudeau’s leadership was already slipping when The Globe and Mail broke the story of the Lavalin affair on Feb. 7. Revelations of Mr. Trudeau’s efforts to personally influence the attorney general’s decision set off a cascade of resignations, including from Ms. Wilson-Raybould, her friend and fellow Cabinet member Jane Philpott, and Mr. Trudeau’s oldest friend and top aide, Gerald Butts.

The government’s ethics commissioner opened an investigation into the prime minister’s actions, and members of Parliament cross-examined witnesses during televised hearings.

Support for the center-left Liberal Party dropped below 30%. As Mr. Trudeau’s fortunes weakened, support for the “small c” conservative alternative was growing. Since 2016, at least six of Canada’s 10 provinces — Ontario, Alberta, Saskatchewan, Manitoba, Prince Edward Island, Nova Scotia and, arguably, Quebec — elected center-right parties. Many were elected because of their hostility toward Mr. Trudeau.

Hanging tough

Even so, political pundits say, Mr. Trudeau will not be easy to defeat and the rally on the right may be short-lived. Andrew Scheer, leader of the opposition Conservative Party, is under attack for impolite statements he made in 2005 when he condemned legalized same-sex marriage because it offended his beliefs as a Christian.

Even while the Lavalin affair was peaking and a carbon tax backed by the Trudeau government raised gas prices by about 3 cents a liter this summer, support for the Liberal Party edged up.

Christopher Sands, director of the Center for Canadian Studies at Johns Hopkins University’s School of Advanced International Studies, said the trajectory of Mr. Trudeau’s government has Canadians reassessing their national brand.

Mr. Trudeau came into power as a “sunny ways” politician, but his time in office has coincided with nasty clashes with China, Venezuela and Saudi Arabia. He was a favorite of President Obama but has had a more complicated relationship with President Trump, although the two leaders were able to reach a deal along with Mexico, after nasty public wrangling, on an updated NAFTA free trade agreement.

“The world doesn’t always have a place for niceness and politeness,” Mr. Sands said.

Despite their attacks on Mr. Trudeau’s leadership, Mr. Scheer and other members of the opposition are struggling to find an overarching argument to make to voters that Mr. Trudeau must go. A Conservative government would repeal the government’s carbon tax and replace it with caps on carbon emissions and fines for polluters. Mr. Scheer also has pledged to take a tougher stand against China, which has detained two prominent Canadians in apparent retaliation for Canada’s detention of a leading Chinese business executive on U.S. charges of violating sanctions on trading with Iran.

But no single political issue is driving this election. Greg Lyle, owner of Innovative Research Group in Toronto, said he expects an atypical, fiercely negative campaign with the Conservatives pushing an anti-Trudeau message to stir up ideological conservatives. The Liberals, he said, are likely to accuse the Conservatives of pushing buttons of social intolerance and denying climate change.

The Conservative election plan is to give people a “reason to dislike Trudeau,” he said.

Mr. Scheer’s Conservatives have solid support in Canada’s western provinces, but that will not be enough if the Liberals hold on in Ontario and Quebec. With their large populations, those two provinces elect 200 of the nation’s 338 members of Parliament.

Canada has three major political parties and two minor ones. As a result, Canadian leaders can win a solid governing majority with just 40% support, as Mr. Trudeau did in 2015.

A record to run on

Mr. Trudeau and his party have some assets as they enter the campaign. The Canadian economy is growing, and the unemployment rate is low. The NAFTA renegotiation sidestepped a disastrous trade war, and the government has another trade pact pending with the European Union. Marijuana was legalized, and Canada accepted more refugees than any other country last year.

Mr. Trudeau’s government settled long-standing aboriginal claims and purchased the Trans Mountain pipeline to ensure it will eventually carry oil from Alberta to shipping ports in British Columbia.

Philippe Fournier, founder of 338Canada.com, an aggregate site for polling data, said the Liberals have a 12-point lead in Ontario and have moved to first place in Quebec. However, a survey by the polling firm Ipsos showed 67% of Canadians want a change of government and only 33% said Mr. Trudeau deserves a second term.

The election is two months away, and a 3% swing in the polls could mean a second Liberal majority or a Conservative win.

“Right now, it’s too close to call,” said Christian Bourque, executive vice president of the Montreal-based Leger market research firm.

Pollsters say Mr. Trudeau may need to draw on his trademark charisma to whip up enthusiasm among his relatively younger voting base because turnout could be critical to the election result.

If the election is close, then West Coast voters in British Columbia will decide the outcome. If Mr. Trudeau’s Liberals win fewer than 169 seats, then he will have to govern with the informal support of one of the smaller parties just as his father did after a second-term setback in 1972.

Ironically, Mr. Trudeau’s former Cabinet members, Ms. Wilson-Raybould and Ms. Philpott, are running as independents. Should they win, Mr. Trudeau may once again need their support.

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