My first thought is that I'd want to limit infantry engagements with hellspawn as much as possible. Seems that armored units, artillery and aircraft ought to handle the majority of contact wherever possible. I'm curious how a slug-loaded 12 gauge would perform against these mythical demons.
They're working on that, however, what are you going to do if/when they manage to open a major portal somewhere like NYC, or even the increasing likelyhood of individual attacks in places like malls.
My second thought is that if I'm fighting against 66.6 million demons and I can open a gate to hell (where most of them presumably still are) for short time, I'm going to be shipping through as many of the most powerful nukes as I can get together. I don't care if most of the good, dead folks have ended up in hell already - they're already dead, and maybe if we send them back to the beginning of the line they'll have a shot at ending up in the right place. Nukes away!
The portal has only been successfully opened once so far, and into the closest equivalent of indignant friendly forces available(some escaped dead souls).
Plus, if you were to invade hell given the assumptions we're making (nasty mud terrain, sporadic/unreliable communication and resupply, the aforementioned 66.6 million demon soldiers who live there) it would seem to be doomed from the start. Logistically, how are you going to keep those soldiers resupplied once they leave the mouth of the portal? Where are they going to get food, water, ammunition, fuel, batteries, spare parts, and all the other logistical necessities required to keep a group of men fighting? Bad ju-ju. Again with the nukes.
Hell's teaming with friendlies held in the equivalent of the biggest, nastiest POW camp ever. With even the forces being diverted right now, we'll likely be able to start freeing souls because the guards are the equivalent of reserves - who are now being called up, leaving gaps in coverage.
Update - it was stated that the 30.06 would have killed it, it was just on it's 'last gasp'.
The demons are generally quite fast on foot, wouldn't we want the extra range rifles give over shotguns? Would 000 buck even penetrate enough at anything longer than 'point blank' ?
But I'll pass on the proposal.