Bad outcome aside, methinks that a large proportion of those who deliver in the ED will be unhappy simply due to their surroundings. Since the number one reason for malpractice claims being filed is due to poor doctor-patient relations, I would think that doing everything in your power to make the mother comfortable would be most important (after stabilizing, of course). Call the OB, document the time and the conversation (especially when they tell you they can't make it in and request that you consult the OB on call or deliver it yourself). Document everything, including the EMS report and why they were brought to your facility. Most times, these deliveries occur in the biggest room of the ED (usually the trauma bay) to accomodate the warmer and NICU/OB team. These are usually the least private rooms in the ED - be sure to draw the curtain and keep the mom comfortable (crowd control).
If you have the luxury of knowing the patient is on the way, hold the elevators and ready a room on th OB floor - you may be able to get the patient there first.
Most deliveries go without a hitch, but any visit to the OB or pediatrician after the delviery can come back to haunt you. Document until you can't write anymore, and whatever is written should save you in the future (assuming you did everything according to standard of care).
Oh, and don't forget - as a resident, be sure to end every note (especially OB) with the simple sentence "Discussed with Dr. So and so, or Dr. so and so aware."
We will all be sued - it is not a matter of if, but a matter of when. I think the hardest part is continuing to practice the medicine you are comfortable with, and not practicing the medicine you think the jury will approve of...