I really doubt you could make a round-trip in time, especially with a taxi (jfk to manhattan is $45, manhattan to jfk could be a bit more). Using the airport shuttle and the LIRR (Long Island Rail) to Penn Station takes about 45 min and costs $12. So a round trip with the AirTrain+LIRR would take about 90 min and cost about max $25.
I really doubt you could