Photo: The Canadian Press

NDP Leader Jagmeet Singh door knocks for his byelection campaign, in Burnaby, B.C., on January 12, 2019.

Even for the federal leader of the New Democratic Party, finding rental housing in Metro Vancouver is no easy feat.

Jagmeet Singh began calling landlords last year as he prepared to move across the country from Brampton, Ont., to run in a byelection in Burnaby South.

"I'd say, 'OK, let me check with my wife.' I'd get back a day later and the place would be gone," Singh said. "The market's really hard out here. If it's hard for me, I can only imagine how hard it is for so many people."

Housing is shaping up to be a defining issue in the byelection, set for Feb. 25, and in the federal election later this year. In Burnaby, renters have been kicked out of older apartments to make way for luxury condos, and sky-high prices are shutting millennials out of the market.

Singh proposed measures this week to build 500,000 new affordable units over the next decade, challenging the Liberal government to start by removing federal tax on the construction of such units. Finance Minister Bill Morneau said the government's mortgage stress test has already cooled overheated markets and it's working on initiatives to help young people buy homes.

On a recent sunny Saturday, Singh knocked on doors inside a co-operative housing complex that is several decades old. The government needs to invest immediately in co-operative and non-market housing and use tax tools to tackle speculation, he said.

"The federal government used to be in the business of investing in housing, hasn't been for decades, and it's something we've got to get back into doing," said Singh.

As for his own search, the 40-year-old politician eventually asked a real estate agent to help. He and his wife now rent the top floor of a house, with a view of snow-capped mountains, above another couple living downstairs.

Liberal candidate Richard T. Lee, a former provincial legislator, said he's lived in Burnaby for three decades and it's an attractive place to live so demand has outpaced supply. The government has introduced a 10-year national housing strategy, he said, worth $40 billion when investments from provinces, cities and non-profits are factored in.

The plan aims to cut homelessness in half, build 100,000 new units across Canada and repair aging affordable housing, Lee said.

"I believe that some of those investments will come to Burnaby South as well," he said.

Lee jumped into the race after the Liberals' first candidate, Karen Wang, resigned after a controversial online post saying she was the "only" Chinese candidate while Singh was "of Indian descent."

The riding is profoundly diverse, with more than half of residents born outside Canada. About three-quarters of those immigrants are from Asia and the top source countries are China, the Philippines, Hong Kong and Taiwan.