The election in the Montreal parliamentary constituency of LaSalle—Emard—Verdun was called to replace a Liberal legislator who quit.
Normally Trudeau's party could count on an easy win there but surveys suggest the race is tight. If the Liberals lose, the focus will fall squarely on Trudeau, who has become increasingly unpopular after almost nine years in office.
Unusually, some Liberal legislators are breaking ranks to call for change at the top. Alexandra Mendes, a Liberal lawmaker who represents a Quebec constituency, said many of her constituents wanted Trudeau to go.
"I didn't hear it from two, three people - I heard it from dozens and dozens of people," she told public broadcaster Radio-Canada last week. "He's no longer the right leader."
Trudeau, who insists he will lead the party into an election that must be held by the end of October 2025, suggested voters would be drawn to vote by anger over elevated prices and a housing crisis.
"Canadians right now are facing difficulties with the high cost of living. They are very frustrated," he said last Wednesday when questioned about the vote and his future.
Questions about Trudeau's future intensified in June after the party lost a safe seat in Toronto in a special election.
Polls suggest that the Liberals will lose badly to the right-of-centre Conservatives of Pierre Poilievre in the next federal election. A Leger poll last week put the Conservatives on 45% public support, a level of broad support rarely seen in Canada, with the Liberals in second place on 25%.
In the 2021 general election, the Liberals won LaSalle—Emard—Verdun with 43% of the vote, far ahead of the separatist Bloc Quebecois on 22% and the New Democratic Party on 19%. Polls now show the three parties are neck and neck in the constituency.
Voting ends at 9pm on Monday (local time). Early results would normally be ready within 90 minutes, but around 80 activists, angry that Trudeau broke a 2015 promise to change Canada's voting system, are also on the ballot. That means counting votes will likely take several hours longer than usual.
Trudeau's popularity has sagged as voters struggle with a surge in the cost of living and a housing crisis that has been fueled in part by a spike in arrivals of temporary residents like foreign students and workers.
Poilievre is promising to axe a federal carbon tax he says is making life unaffordable and last week vowed to cap immigration limits until more homes could be built.Liberals concede the polls look grim but say they will redouble efforts to portray Poilievre as a supporter of the Make America Great Again movement of former US president Donald Trump as an election approaches.
Poilievre, an acerbic career politician who often insults his opponents, also says he would defund CBC, Canada's public broadcaster. In April he was ejected from the House of Commons after he called Trudeau "a wacko".
