This is a difficult question to answer, because it's not a black and white answer.  First of all, not all heroics are created equal, some (like Slave Pens, Underbog, Botanica, etc) are fairly easy, even without a perfect group, while some (Shattered Halls, Magister's Terrace, etc.) can be difficult even with a well geared, well balanced group.

That said, assuming you're going for some of the easier ones, and you have a good group that's equally geared, a priest can probably pull it off at around 1100-1200 Healing, but that would probably involve a couple wipes even in some of the easier ones.  I'd say to be comfortable, you'd probably want to see more like 1400-1500.

All you have to remember is that the Heroics are generally about a half-step behind Karazhan in terms of gear requirements and rewards, so if you can run one, chances are you can run the other.