I'm actually not sure, since I'm a Canadian :D But, I have friends and family in the US who have gotten second opinions with no problem. Usually, if the relationship is good with the first specialist, and s/he is very professional, then that first specialist will have no problem with a patient getting a second opinion. So, I would say that if you get along well with your surgeon, then you should probably keep your first surgeon in the loop and let him or her know about the second opinion. If you're uncomfortable with that, then it might be possible to just ask your primary doc to get a second referral and not share thata with your first surgeon.
Please take these suggestions with a grain of salt, though, because we do have a different system up here! Perhaps some folks from the US will come on soon and give you first-hand advice.