Well for a start, I think there's a balance to be had. A ratio, if you will, of the comparative quality of gameplay to story, in which I think the gameplay is the more important component to keep a person's interest. To more directly answer the question, I will admit that a bad story is a bit offputting, but the worst it's made me do is stop playing for now, whereas bad gameplay can prompt me to stop playing entirely.
Case in point, the world's least credible frame-job in Dishonoured I found almost insulting - I think it was supposed to make the player feel some sort of righteous indignation, but the fact is a child could've seen through that feeble frame-up (I think in this case they stretched my suspension of disbelief too early). Back on topic though, I played the intro, switched that crap off, then came back a couple of days later and enjoyed it much more on the second attempt. Just a wild idea, could it have been better by skipping the intro and leaving it a mystery, letting players figure out for theirselves whether Corvo was guilty or not?