DFW to ORD is $11.23 in coach, one way.
DFW to LAX is $12.70 in coach, one way.
LAX to JFK is $19.26 in coach, one way.

That should give you an idea. It may not sound like much, but that can really add up.

Don't forget about getting a crash pad or buying a hotel room a couple of nights per month. Being on reserve for days on end means you can't bring a lot of perishable food, so expect to pay for a couple of high-priced airport meals. Also think about what your time is worth and how far you may have to commute.

I did SEA to ORD for 3 years. I made it work, but now I live in base and couldn't be happier.

Edit: Don't forget that Eagle pilots fly for free on other airlines. If a different airlines serves your city, that is your ticket. Also, if you sit in the jumpseat on AA or AE there is no charge. Then after 5 wonderful years, coach seats are free! Hold your breath.