That is quite a dilemma, he is gonna have to poop eventually. Is this the same dog in your profile pic?
No, that's my older one. He's way too slow to catch squirrels, and (mostly) willing to hold still while there's a rabbit on his head.
I'd call a vet. Too be fair all the vet is going to do is tell you to watch him and make sure he poos. If he does stop, take him to the vet immediately.