Hi,
My understanding was that, as a student at least, you required a US (FAA) medical to fly in US airspace. This is far less stringent than the JAA class 2, so should be no problem if you already hold a european medical.
I had my FAA medical done at med-fly next to the pilot shop at the airport, and IIRC it cost about $85. It took about 10 minutes. Ask for the version of the medical card with the "Student Pilot Certificate" on the back, as this can also be used for endorsements from your instructor.
Peewit - Don't bend N946AC!
I did my first solo in that aircraft and will be needing it again in a month or so. Good Luck!