MONTREAL—With pressure mounting on Jagmeet Singh to enter the House of Commons at the earliest opportunity, the rookie NDP leader is apparently seriously considering a run for Thomas Mulcair’s soon-to-be-vacant Outremont seat.

Winning the Montreal riding would be a big deal. A Singh byelection victory would assuage fears that on his watch the NDP is at risk of returning to its non-starter status in Quebec.

It would shatter the Liberal assumption that Justin Trudeau can count on his home province to deliver enough gains in 2019 to make up for seat losses elsewhere.

It would contrast nicely with Conservative Leader Andrew Scheer’s bylection track record. He has lost two seats to the Liberals since succeeding Stephen Harper a year ago.

And if all of the above sounds almost too good to be true, it is because it probably is.

Sometimes a remedy is more potentially lethal than the ailment it is meant to cure. On the risk scale, a Singh run in Outremont would fall somewhere between bold and reckless.

It is not that the former Ontario MPP would be the first incoming federal leader to look for his first House of Commons seat outside his home turf.

Brian Mulroney, Jean Chrétien and Joe Clark in his second incarnation as Tory leader all initially ran (successfully) in byelections in Atlantic Canada. They returned to their respective provinces in the subsequent general election.

But no party has tried to parachute an out-of-province leader in Quebec, let alone in a riding that hardly qualifies as a safe seat.

Before Mulcair scored the first of four back-to-back victories in Outremont in 2007, the riding had a near-perfect Liberal track record.

At the time his political pedigree mattered more than the party under whose banner he was running.

As a recent member of premier Jean Charest’s provincial cabinet and as a longstanding Liberal MNA, Mulcair brought more Liberal credentials to the byelection fore than Stéphane Dion’s handpicked candidate Jocelyn Coulon.

Overall, Mulcair offered Outremont voters a relatively seamless transition from the Liberals to the New Democrats. Those voters include a significant Hasidic community that has found comfort in his strong pro-Israel convictions.

But with the former NDP leader out of the picture, the byelection that could be called as early as this summer is widely considered the Liberals’ to lose. On Trudeau’s list of winnable opposition ridings in Quebec, Outremont sits at or near the top.

As recently as February, New Democrat insiders were bracing for a near-inevitable defeat in Outremont. At the NDP’s national convention party spin-doctors were already at work lowering expectations that the party, post-Mulcair, would hang on to his riding.

Since then though Liberal fortunes have taken a hit in the polls and a leadership crisis has sent the Bloc Québécois into free fall. But neither of those changes is necessarily of such magnitude as to fundamentally alter the Outremont dynamics.

Ontario and not Quebec has been the ground zero of the federal Liberal decline in voting intentions. In his home province, Trudeau still enjoys a double-digit lead on the competition.

As for the orphan supporters of the BQ, in the last election they voted for a party that campaigned hard for a veil ban at Canadian citizenship ceremonies. On that basis, they probably make up one of the constituencies least inclined to shift to an NDP led by a turban-wearing politician.

Outremont is a diverse riding but that does not automatically translate into an edge for a visible minority leader such as Singh. Trudeau who has consistently championed religious freedoms over the course of the province’s secularism debate is popular in his own right within Quebec’s cultural communities.

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Singh’s lack of a federal seat is undoubtedly hurting the NDP. It is hard to participate fully in the national conversation from the public galleries of the House of Commons. Politics is not a spectator sport and a leader who is just visiting can’t help but come across as a parliamentary tourist.

Most of the MPs who serve under Singh did not know him well prior to his federal run. They have all spent more time in the federal arena than he has. Singh’s absence from the House is not conducive to the necessary bonding that needs to take place between a caucus and a new leader.

But in that fragile context a Singh defeat in Outremont — especially if it were decisive — would inflict further damage to party morale as it looks to a general election. It could only lead to more questions as to the leader’s judgment. In politics, the line between a leader who is walking wounded and one who is a dead man walking is often a thin one.

Chantal Hébert is a columnist based in Ottawa covering politics. Follow her on Twitter: @ChantalHbert

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