Incorrect country of birth on passport...

I'm a recently naturalized citizen in the US. I am traveling to Brazil in two weeks for surgery and only just realized that my new passport says I was born in the city and state where I currently reside, not the country where I was born.

I'm freaking out. Has anyone had this happen? My naturalization certificate has the correct country, but if they ask me for a birth certificate, I don't have one at the moment and am screwed. I'm driving 4 hours to my closest passport office (sob) later this week to see if they can correct it in time. I don't know if I should do that and hope they get my corrected passport to me before I fly, or just travel on it.