The $45 flat rate to Manhattan is for taxi only. Limo will charge more, $50-70+tolls+tip depending on the type of limo. You would need to book a limo to pick you up, or inquire about a car service (not a limo but a nicer than a taxi) at the Ground Transportation counter. Try Carmel Limo www.carmellimo.com as they do alot of pick-ups at JFK.
The $45 flat rate to