Did they ever have any problems before? Has any party similar to the current version of the GOP gained power in Canada?
In a lot of ways, the Canadian Prime Minister has more legal power than your President. We don't have the division of powers that you do.
@9-10ths_Penguin is quite right, a Canadian PM does have a lot of power. On the other hand, we don't need to resort to impeachment proceedings to get rid of one -- we can do that over tea with a non-confidence motion in the House.
@Stevicus, I am not aware of any party having tried to overturn the norms and standards of this nation. But we're so boring: our biggest precept for making Canada a nice place is POGG (Peace, Order and Good Government). I'm told our favourite colour is grey (don't want to offend). But do you know what the capital of Canada is? Mostly American!
No, we are really a very different entity up here. Not surprising, since it's colder, I guess (you should try growing up in our actual Capital, Ottawa -- I did). With a multi-party system, and a parliamentary government, we mostly have enough opposition to, if not stop government overreach, at least slow it down.
Now, admittedly, this depends a lot on the personalities. Right now, a minority party (New Democratic Party) is supporting our minority Liberal government so that basically they can do what they want. However, should they do something egregious, any supporting party wanting to stay in the business of government would act accordingly, and since the Liberals hold only 157 of the 338 seats in the Commons, well, as I said, defeat can happen over tea-time. (If the governing party in Canada loses a vote declared to be a "confidence motion" in the House, the government is defeated and the Governor General can call an election.)