Justin Trudeau came to office in 2015 by the high road, exuding charm, confidence, integrity and an openness to change. He filled his cabinet with women and minorities, opened Canada’s doors to immigrants and posed for endless selfies with adoring crowds. But in politics the fresher the face, the more obvious the blemishes.

With seven months to go before Canada’s next national election, the prime minister is embroiled in a political scandal that his charm cannot wipe away. Two members of his cabinet, both prominent women, have resigned, as has his closest adviser, and unless he can convince the public — and do so soon — that he really did nothing wrong in trying to head off the criminal prosecution of a big Montreal-based company, the damage will only get more serious.

The crisis unfolded after The Globe and Mail newspaper reported on Feb. 7 that Jody Wilson-Raybould, Mr. Trudeau’s former justice minister and attorney general, had come under improper pressure from the prime minister’s office to reach a negotiated settlement with a multinational engineering firm, SNC-Lavalin, instead of prosecuting it on criminal charges it faces over its business dealings in Libya. Conviction would bar it from government contracts for a decade.