The pain of having teeth pulled and gums prodded for denture fittings was followed by relief at the payment counter: The $4,000 worth of work would cost Ron Brydges nothing under Canada’s new national dental care program.

“This dental plan being free was just a godsend,” said Mr. Brydges, 84, a retired industrial mechanic in St. Catharines, Ontario.

For that, Canadians largely have the leftist New Democratic Party to thank.

Subsidized dental care is among several social programs, including a national drug plan and protections for striking workers, promoted in recent years by the New Democrats that have augmented Canada’s reputation on the global stage as a liberal bastion.

“I view all these things as investments in people, not expenses,” said Mr. Brydges, a New Democrat supporter. “It makes us a better country.”

But today the New Democrats are being severely tested, with questions swirling about the party’s very existence as Canada heads for national elections on April 28 amid a rupture with the United States, its neighbor and closest ally.

The resignation of Prime Minister Justin Trudeau and President Trump’s economic assault on Canada have set off a tectonic political shift, leaving the New Democrats, and their leader, Jagmeet Singh, with dwindling support.