With regards to cost:
As as attending+resident, you'll be able to afford it, though the specifics is going to depend on where you live.We had our first baby when my wife was in residency in a medium cost-of-living US city. My wife's program let her have 12 weeks maternity leave, of which she took 11 (since taking all of it would have meant she had no vacation time). My baby started daycare at 11 weeks. That ended up costing us right around $1000/month for a daycare where the kid was there from 7a-6p.
If you look it up, $1000/month is around the nationwide average for daycare, but that includes a lot of cheaper areas. We've since moved to a much higher COL area and are paying $2000/month for a very nice daycare (and it's now 830a-6p, but that's because my schedule is lighter). Could probably have found things $100-200 cheaper, but not by much unless it was quite far from where we live.
But you have a bigger problem than cost: Scheduling. The above worked for us because I have a M-F clinic schedule without call - so if my wife was on nights or on a 24-hour shift, I'd be able to take care of the baby. Obviously your own surgical residency schedule is totally wackadoodle, but your wife is in EM. Even in an academic setting, as far as I know people in EM still have to work periodic nights and weekends. What's going to happen when you both end up working on a Sunday? Or overnight? There's no daycare that's open at 3am on a Tuesday.
So while daycare is the *cheaper* option, it's likely going to be unworkable at least part of the time due to scheduling issues if your wife's shifts coincide with yours. If her group is flexible, then maybe you could pull it off, but you need to be pretty sure of that.
So where does that leave you? Well, nannies. But given the very variable schedule of needs, you might have trouble covering everything with just one. It sounds like your wife works 3-4 shifts a week and has an ungodly commute on top - lets pretend they're 8 hour shifts plus 2 hours of commuting (and she gets out on time) - that's going to be at least a solid 40 hours on weeks where your wife's shifts all overlap your work schedule. Average nanny nationwide makes just over $15/hr, so that's around $30k a year, but there's taxes and things that will bring that up to at least $35k. And you probably won't be able to get a nanny with a schedule like that making just $15/hr - not to mention you might not want the cheapest option. But even if you're double that, a two physician household where one is an attending can definitely afford it. Even if you have to hire two separate nannies and coordinate schedules between them.
One thing you may want to look into is au-pairs, which some of my colleagues have had good luck with. They're live-in nannies that are somewhat of a cultural exchange program with other countries, and you can ask them to work nights and weekends or anything else as long as you don't exceed 45 hrs/week. Total cost is around $20k plus you have to provide them a room to stay in, food to eat, and some form of transportation - but you get a fair bit of flexibility from there.