Yeah, if the barb broke... it is only a matter of time. The tubes inside the core are thinner than the feed lines are.
Having pulled an XJ dash before, I was able to do my first late-model heater core in 4 hours flat. Betting I could do the next one in 3 hours. Budget an entire weekend if you haven't done one before, mostly so you have time for a frantic junkyard run if you break a brittle plastic piece halfway through.
Oh, the studs that hold the HEVAC box to the firewall are a bastard. Clean the threads off well before you attempt to unscrew the nuts and use penetrating lube. They like to back the other end of the stud (coarse self tapping threads into the plastic HEVAC box) out of the plastic instead of unscrewing the nut. There are a few of them, on a late model there are 5-6, two are behind the engine slightly to the passenger side. You'll want an 11mm flex head gearwrench to get at them, it makes it much easier.
This is all late model specific, it may also apply to an early model but I am not sure.
While you have it out, toss a new AC core in there too. It's in the same housing, so might as well, since you'll be a few hours into the project anyways.