The point set topology and understanding of the reals necessary to prove the "backbone" theorems in calculus in their usual form are only one of the obstructions facing the students as they move from calculus to real analysis. Being able to work with O and o seem to be very hard for freshmen and sophmores as well. it would be nice if the students got some idea of the rate of growth of a function or the rate at which it tended to zero in their precalculus courses. A good intuitive feel for these ideas would make it mucheasier to teach the kind of midway course Michael was calling for.
For almost all freshmen the standard honors course (Spivak or a facsmile) is a deadend. They really don't have the background to see why these issues are worth grappeling with even when they succeed in mastering particular ideas. It would be better to recapture the spirit of the 1700s whne mathematics was being used to "blow away" physical problems. Allowing the need for rigor to emerge naturally from these successes would produce a great first real analysis course.Best, Terry Gaffney