you don't impeach Canadian Prime Ministers
however, voting in Canada is very different from here
Trudeau needs to go though, but he just got voted back in...far less popular than he was at first
he's made a mess of Canada's finances and the dollar has fallen so low you have to look in the ditch to find it
Our deficit is insane, but the debt hasn't ballooned in Canada as badly has it has in other countries including the United States where its reached over 100% when measured as Debt to GDP. In Canada our's is in and around 30%....and its that justification that Trudeau's Liberal government has used to rationalize breaking the 2015 election promise to balance the budget.
Parliamentary democracy is very different from the US Republican model, in point of fact Canada doesn't directly elect the Prime Minister. We've even had a couple within the last 40 or so years who became Prime Minister after the sitting PM resigned...John Turner and Kim Campbell.
In a nutshell here is how it works. Canada has 338 ridings, which are basically like US Congressional districts. In each riding or district parties run candidates....we have the Conservative and Liberals, and one or the other has won every federal election in our history. But there are other parties as well, the socialist or labor centered NDP, the Green Party....and then some smaller parties, Christian Heritage Party, Communist Party,
Anyway all the parties can run candidates in each riding....and the person who wins the riding is the person with the most votes, they don't have to be at 50%+1.....just the most, we call it "First Past the Post" or FPTP for short. So in a riding with a Liberal, Conservative, NDP, Green and a People's Party candidate....its conceivable that the winner might only get 25% of the total vote.
Anyway after the election the winning candidates form our House of Commons, much like the US House of Representatives. Whichever party has the most seats forms the government, and the leader of that party becomes Prime Minister. If the winning party has over half the seats they can run basically unopposed....they can do what they want.
Lots of people talk about Hillary winning the popular vote in your last election. In Canada Trudeau, like Trump, lost the popular vote....Liberal candidates won roughly 33% of the vote while Andrew Scheer's Conservative candidates won about 34%. The remaining 33% were spread between the other parties NDP, Greens, a party called the Bloc Quebecois which only ran candidates in the province (state) of Quebec....there was also the People's Party which got 1.7% of the vote (the party I voted for) and a whole mess of smaller parties. We even had one independent candidate elected.
Of the 338 seats in our Parliament (again, similar to your house of reps) the Liberals took 157 seats....which is 13 shy of what was needed for a majority. That means that in order to pass legislation they'll need the support of at least 13 other members from other parties. In Canada most votes follow party lines....so Trudeau will need the support of either the Conservaties who have 95 seats, or the Bloc with its 32, or the NDP and its 24.
I'm Canadian but I spent a lot of my younger years growing up in the United States, (NY, NJ and Oregon) and I'm a bit of a political junkie so I understand the two systems fairly well....not perfect but pretty darned good.
I'm looking forward to the US election next year, if you divorce yourself from caring about the outcome it can be very entertaining.....