you shouldn't need to show your passport as it doesn't involve going out of the country and proving which country you are a resident of. The Orange County Fl website should have all the info about applying for your marriage license I don't even remembering it saying anything about a license....But, I'm sure if you just include your social that is all it might take...?
I just did the mail away marriage license from Brevard county. On the forms they ask you for your social security number and a form of picture ID to send along with it. We sent a copy of our driver's License. Also when we went in front of the notary they asked us to show our license as ID. We didn't have to do anything with our passports. HTH.