That would represent about a third of the Liberal caucus, which has 153 seats in Canada’s House of Commons.
nationalpost.com
There absolutely is a mechanism.
The PM serves at the pleasure of the GG on the understanding that he or she has the support of the majority of the House of Commons. Conventionally that individual comes with the backing of a party.
Ultimately the fate of the PM rests with the House of Commons and whether or not he or she has that majority.
Patently this PM has lost his majority
103 Trudeauite Liberals
50 Non-Trudeau Liberals
120 Non-Trudeau Conservatives
33 Non-Trudeau Bloqistes
25 Non-Trudeau NDP
2 Greens
4 Independents
1 Vacant
Poilievre was quite within his rights to bring this matter to the GG and request an opportunity to form Government. The correct response, in my opinion, then becomes, because it is not clear that the house would support Poilievre anymore than it would support Trudeau, and the parliamentary term is so close to completion, a general election.
The issue is not in Trudeau's hands. It is in the hands of the Commons and the GG.
Loss of an election triggers a Liberal leadership review.
There is a mechanism.