I've been running EotE for a few months now, and so far, player obligation has stayed roughly the same. The big obligation is a group debt to a crimelord, and I'm in the middle of putting the group through a mega-adventure designed to recover a gem the crimelord lost that will get rid of their obligation. Outside of that, though, not a lot seems to be happening as far as gaining and paying off Obligation.
How are other GMs handling this? Do you have adventures set up specifically for players to pay down their obligation, or do your players tend to want to pay down their obligation naturally?