Unlikely.
Consider flying from Cleveland if the flights work better and parking your car for ~$6/day?
This is what I got, probably have to leave 5 hours before flight leaves CLE.
Cleveland, OH (CLE) to New York City, NY (JFK)
Departing
Hopkins Intl Airport
Mon, May. 04, 2015 at 5:00 PM
Arriving
John F Kennedy Intl Airport
Mon, May. 04, 2015 at 6:43 PM
Layover Time: 5h and 8min
Departing
John F Kennedy Intl Airport
Mon, May. 04, 2015 at 11:51 PM
Arriving
Ben Gurion Airport
Tue, May. 05, 2015 at 5:35 PM
Departing
Ben Gurion Airport
Tue, May. 12, 2015 at 12:10 AM
Arriving
John F Kennedy Intl Airport
Tue, May. 12, 2015 at 5:14 AM
Layover Time: 4h and 31min
New York City, NY (JFK) to Cleveland, OH (CLE)
Departing
John F Kennedy Intl Airport
Tue, May. 12, 2015 at 9:45 AM
Arriving
Hopkins Intl Airport
Tue, May. 12, 2015 at 11:35 AM