I like to extend my primary for more than 2 weeks, and I've found this is the #1 reason my beers have improved from when I first started. I left my arguably best beer, a bourbon chocolate stout, in primary for 7 weeks, although that was a little higher in the ABV department than some I've made.
So 2 weeks can be enough, but I think more time can only help in most instances. (I brewed a wheat last summer that I think I left on the yeast cake a bit too long, but I also didn't have good tempurature control, so can't pinpoint the cause of the funky flavors exactly.)
As for carbing, if the room is warm enough, 2 weeks has been fine in my experience, and 3 weeks is even better.