I have faced this exact situation before. There are several issues to consider:
1. From a schedule standpoint, for most IM programs this isn't a huge deal. Most categorical programs are going to include some elective, outpatient, or other non-call time. As I'd know right up front that you need this leave, I'd simply arrange your schedule such that your less stressful time is put at the front of the schedule. This adversely affects no one, except you -- as the second half of your year is going to be more busy. It's possible that a program's schedule would be so tight that they can't handle missing an intern for 2 months -- but in my opinion that's their problem, it's best to plan for a bit of wiggle room. Other fields might have a very tight schedule where it would be a problem, IM is usually not a problem.
2. Exactly "what happens" depends upon whether you can actually start before you have your baby. Remember that orientation probably starts in mid June. If you can get to orientation (esp if you can get through orientation), then you can probably claim disability for your maternity leave and get paid. The program can't not hire you because you're about to have a baby. If you actually go out in the middle of orientation, I have no idea what happens -- you might not actually be "hired" then. If you have the baby before orientation, then you will need a late start. In that case, you won't have any pay / benefits until you start. Again, because my intern schedule iincludes some elective or outpatient time, I can relatively easily start you late, the other interns would be on the call blocks, and your call blocks would come later. Sounds like you'd have insurance through your husband, so this might not be an issue.
3. Could a program waive your match because you deliver before orientation starts? Probably not for this reason. As long as your pregnancy leave wasn't going to be very long, I highly doubt the NRMP would allow a waiver. In any case, I highly doubt any program would ask for one. It would make terrible press. Totally different issue if you were to say you wanted 6 months of leave to start
4. Is starting late bad for you? Not really, especially if you're only going to start 6 weeks late. We have interns start late all the time, and it's really not a problem.
5. Is taking only 6 weeks off for a new baby a good idea? That's an impossible question to answer. I've had residents who come back after 6 weeks with no issues. I've had residents have marked emotional distress even after 12 weeks. As already mentioned, you'll need a 100% solid child care plan. In fact, you'll need two child care plans -- one for backup in case the first fails. Once you're at work, you need to be reliable.
6. The other problem to worry about (unfortunately) is pregnancy complications. If you develop something that requires bedrest, you might not be able to finish medical school (although these types of complications usually occur late in pregnancy, so hopefully will not be a problem). But if your graduation is delayed, that would obviously result in you losing your match.
7. Even if, somehow, you match somewhere and then can't start, get a match waiver, and then apply for the match the next year, you're going to be fine. You'll tell this story, and no one will care. In fact, I'd be pretty upset at a program that dropped you for this unless your start was delayed more than 4 months. And if your delay becomes that large, something has happened where you'd probably be better off delaying a year anyway.