Silverknapper,
There is no such thing as an FAA ATP issued on the basis of a JAA ATPL. You may have used your JAA ATPL to meet the pre-requisite of a US Commercial Pilot certificate (as allowed by 14 CFR 61.153(d)(3)), but your FAA ATP was issued on the basis of you meeting all the requirements for the FAA ATP, including a written and practical test, along with meeting all the aeronautical experience requirements.
It sounds like you did your ATP practical in a multi-engine airplane, so you would have a FAA ATP with a Multi-Engine Land Rating. You would have no single engine privileges at all since you have never demonstrated your single engine prowess to the FAA. In order to fly a single engine airplane in the US (even at the private pilot level) you will have to take a checkride in one at any of the private pilot, commercial pilot or ATP levels (your choice).
And if you're thinking about getting a FAA Private Pilot certificate on the basis of your JAA ATPL with single-engine privileges, you're out of luck, since you already hold a U.S. pilot certificate they will not let you do that.