It is difficult to explain the difference between 23 NY to NJ miles then 23 miles on a freeway in your hometown. Unless they have experience in this area, they will have no idea what could happen in between!
I have had to face the opposite problem from time to time; there are often more convenient non-stop flights for me out of EWR, but living on Long Island there is absolutely no way that I would ever choose to make the trek to EWR, even though once there the convenience factor (not having to make connections) might be great.
You should give your travel folks these facts:
1. You will be adding time because of toll both backups (as previously mentioned) as well as adding money because of the added tolls between NY and NJ and return;
2. Depending on the time of your return to LGA (assuming you booked a round trip in and out of there) could be dicey as well. Traffic heading East is often worse then the traffic heading west;
3. The 23 miles between the 2 airports can actually take several hours, even in the middle of the day.
The overall cost savings will be mitigated by the stress and potential delays.
Just my 2 cents...