Holy Cow!
The OP's travel agency should have their licenses revoked, as they are clearly incompetent. I'm guessing they are completely unfamiliar with NYC.
It would be one thing if they had booked the OP from DFW to LGA and then a JFK departure, as that change-of-airport connection is done all the time, and is doable with three hours on a Friday afternoon.
But Newark to JFK? Only a moron would sell their client that kind of itinerary.
Yes, I've done it, but on itineraries I purchased on my own, not as a travel agent. With limited bags, extensive knowledge of the region and its trains, it's possible but it's not for the uninitiated. In the 1980s, DCA-EWR could be bought for $19 to $29 on PeoplExpress, providing a cheap way to get to NYC for a JFK departure 3-4 hours later. Fun adventure when you're by yourself and the stuff that great travel stories are made of. Sheer lunacy to ever suggest that anyone else do it, especially for a travel agent to suggest it.