I'm feeling the pain too--not that I've gotten around to doing anything about my application yet...
It's best to talk to your advisor (hopefully from an EM residency) to get an idea of how competitive you are, how many to apply to.
I've also been told that it's better to be safe and err on the side of too many, then turn down interviews if you need to. BUT always tell them promptly when you decline--it's a small enough community and people talk!
Good luck! ERAS procrastinators unite!