You can obtain a FAA license issued on the basis of your EASA licence, commonly referred to as a "piggy back" licence issued in accordance with 14 CFR 61.75. This depends on your ICAO licence being current and valid in all respects, and is issued as a FAA Private (restricted) certificate.
Airmen Certification ? Verify the Authenticity of a Foreign License, Rating, or Medical Certification
Otherwise, you may be referring to the long awaited US-EU BASA agreement which is due shortly. This will (initially) allow private pilots and instrument rated pilots to obtain a FAA license on the basis of a EASA licence and vice versa with fewer conversion requirements than at present. The draft agreement is on the FAA website:
http://www.faa.gov/about/office_org/...ng_Summary.pdf