What you're leaving out, in Canada's case, is that the norm is a strict party-line vote. In rare cases, the PM will allow a "conscience vote", where individuals vote as they will; in every other case, you vote as your party directs or you're kicked out of the party. As party-line voting is the norm, sitting as an independent is basically worthless in terms of accomplishing anything--no access to party resources or assignments.
So in practice, the PM of a majority gov't (i.e., has a majority of seats) gets to pass whatever they want to pass; the saving grace of this is that, without having to haggle and herd cats and trade horses, the legislation is the legislation--there's no poison pills, no payoff amendments, no loopholes to capture one person's support, and no extreme bits to trade away. It's just "this is the law we want", which I think leads to higher quality legislation over all.
The PM of a minority gov't (i.e., only has a plurality of seats) may have to secure another party's vote to pass, but that's a negotiation with a second entity, not a hundred other voting entities.
Consensus doesn't play a significant part in it, I believe. Within the bounds of the law, the PM of a majority is nearly a polite dictator.