Does God (always) give sufficient grace to avoid temptation?

I've often taken comfort, and sometimes guilt, from 1 Cor. 10:13. It's the "(for any temptation) God will provide a way of escape" passage. As a future-oriented promise, it gives me hope. But when I consider past failures in light of it, I think "you idiot! you could have escaped!" So, is this true? For the Christian, is it true that, for all past temptations, if I had simply availed myself of the divinely-provided escape hatch, I would not have committed the sin? What of the future-oriented version -- for any temptation that I will face, it is possible for me to overcome it. True?(Where 'possible' here means more than logical possibility -- it means 'within the capabilities of an ordinary human, given the grace provided.' That is, it would not require some Herculean effort on my part.)

Alexander Pruss prompted my thoughts on the subject with this excellent post.