I mean, yeah, it's technically the right thing to do. But it's just shy of impossible to implement, and it presents a goofy user experience to your users.
So if all your thing does is post stuff to Twitter on behalf of your users, I think it's probably best to save yourself 40-odd hours of frustration and perplexity, and simply save their user/pass in your database. It is, after all, just somebody's Twitter account, not their banking credentials.
If you're logging into something where money can change hands, then yeah, go nuts and do the right thing. But not for some throwaway-password site where the worst thing that could possibly happen in the case of a compromise is that somebody whinges about their cat in one of your users' name.