Ok, first off:
I concede that there is apparently less munitions in stock currently held by the US military than the sheer numbers of the German Wehrmacht. I'm not familiar with numbers like that (munitions info), and well, 12 million plus is a BIG number to take stock of.
It doesn't change the massive technological disparity. Our strikes can be far more targeted and precise than theirs. We can hit them day and night from any direction using infrared, laser, radar satellite and TV-guided targeting. They will really have no way of protecting their armaments other than surrounding them with hostages or deliberately placing them within areas with a heavy civilian population, which could well rankle their ethics.
Regarding resistance by police, there is little data to actually present as most department websites don't mention numbers. Here are a few that I was able to find:
APD: 2,000 officers
Henry County Police: 229 active, 14 reserve
Johns Creek Police: 62
Now bear in mind that there are at a minimum 146 cities and towns inside the metropolitan Atlanta region, from twenty counties, with a total of over five million people population. Where I live in McDonough, we have Henry County PD and HC Sheriff's Dept. A few miles down the road, we have the City of Griffin PD, City of Hampton PD, City of Stockbridge PD, City of Locust Grove PD. That's leaving out the public school police departments (yes, we have those).
This is pretty typical for most counties within the Metro Area-- you have individual city police departments, which tend to be fairly small (30-100? officers, depending on size of city/town), then county police departments, then other departments such as the sheriff's department. There are also a good number of colleges and universities inside the metropolitan area, all of which have their own campus security forces. There's a FBI office inside town and a Secret Service Treasury Department posting. Also state forces such as the Georgia State Patrol, Capitol Police and GBI, which admittedly will be spread out through the state to some degree but their headquarters are in Atlanta.
So 2500 cops in metro Atlanta? I don't think so. Closer to 3 or 4 thousand if you add them all up. Possibly as many as 5,000. Does that make them a barrier to the Wehrmacht? Not really, no. I never said they would stop the Germans or even win (seriously, wtf?). All I said is that they wouldn't just sit back and let the Germans roll over them.
Now if the Wehrmacht's general staff decides to play nice, send a few soldiers in unarmed with white flags and a carefully worded message... they could perhaps get the cops to surrender before picking a fight, on the basis of "we have waaaaaay more guns than you and if you decide to throw down things are gonna get messy, son". Facilitating a peaceful surrender of the city would be a quick way to keep civilian and police resistance down, as the sooner they can get, say, the Mayor on the air broadcasting "people, sit down, shut up and don't shoot the people in the grey uniforms," the sooner they can focus on reinforcing their position against the inevitable assault to come.
As I said earlier, the only way for them to really protect themselves from our ability to reach out and touch them from a long way away is to hide among the civilian population. A population that will be going "hey what just happened..." and coming to the realization that they are being occupied by a hostile force. Something that doesn't tend to sit well with anybody. And considering the numbers for gun ownership in the American South, and the amount of crazy we've got... well, the Germans probably won't be sitting easy after a while even if they manage to force a peaceful surrender.
So the ways it can go down:
--Germans occupy Atlanta. With or without resistance, it's a given they can take the city and metropolitan area. Nobody's disputing that. Long run (space of days? weeks?), they lose. It'd make a mess, though. Either way (resistance or not) lots of civilians are probably going to die from collateral damage if nothing else.
--Germans surrender more or less quickly once they realize the massive technological disparity. Not really in the parameters the OP set forth, IMO, as Zor explicitly said the Luftwaffe were on their way to bomb bases. Probably going to take a few tanks blown up at 4 km and a few well-placed bombs or missiles first, though.
--One scenario we didn't cover: the Wehrmacht decides to make its way overland. To where? Who knows. They could hole up in the Appalachians or the Smokies if they went up to Tennessee or the west Carolinas, although it's 101% certain that from a few hours, if not minutes, of their appearing the US would have eyes on them the whole time. Regardless, they are leaving the relative safety of Atlanta's civilian population and basically becoming a massive target-- even more liable to get hit by a tac-nuke or a few daisy-cutters. So if they decide to leave Atlanta, and if they know our capabilities, it's a fair guarantee they'd either surrender or go guerrilla. *That* could be a real pain in the arse to root out.
Thoughts on the Luftwaffe:
The German aircraft are largely useless in this scenario other than ground attack and some interdiction of the Atlanta area's airspace, and unless the Germans brought plenty of fuel along, that's going to become a crisis for them quickly until they secure the supply of gasoline.
A quick Google shows that they used 87-octane gasoline at the start of the war; this can be procured from gas stations, tanker trucks, and such. There are certainly fuel depots around Atlanta that would be worth securing for their purposes. Jet fuel is probably useless to them, which is a shame as there's plenty of it around Hartsfield.
Air-to-air is a bust for them other than lucky shots; apart from the 262 and *maybe* the He 162, the Luftwaffe has no aircraft anywhere near as good as American combat aircraft. Even our bombers fly far faster than their fighters. All they have are cannon and unguided rockets for the most part. I can see them shooting down some drones, but the only thing they can really do, other than being targets for the USAF, is...
Air-to-ground: a far more viable role. While they don't have anywhere near as accurate munitions as the American forces, strafing, bombing and dive-bombing are still tactical options available. They can do some area denial in the form of bombing roads and bridges, attempt precision strikes against tank formations, try to blow up some trains, strafe soldiers, and so forth. They will lack real-time communications with forward troops (? not sure about this) but can still be useful tactically and strategically.
I cannot say that I am versed in US AA doctrine, but I believe it's largely missile-based nowadays. This may be an issue with low-speed propeller engined aircraft... if only for the reason that there are so fucking many of them the Army might actually run out of Stingers. If they had M163 vehicles with Miniguns still around, might be a good time to pull them out of mothballs but I doubt it. Would be a good time to quietly ask Russia for the loan of a few ZSU-23's.
Tanks and armoured vehicles? Tough targets for infantry, but can't really touch ours. Never mind that we've got anti-tank helicopters and aircraft, a category that didn't really exist in the 1940s and that the Germans won't really know how to counter. Their tanks will die, quickly.
Their infantry is using bolt-action rifles for the most part (unless you go with scenario 2, which gives them StG-44's). No body armour to speak of other than helmets. We've got plenty of body armour; our rifles tend to be lower caliber, but boy can we shoot a lot faster than them. Their only real advantage is numbers-- they've got a lot more soldiers than we do. In fact, they have so many that they might be able to take advantage of full-blown human-wave assaults to overpower initial attacks.
And that could be their biggest weakness, because you can damn well bet we aren't going to let their logistical forces supply them from outside their perimeter. So it could well turn into a siege. Twelve or thirteen million men, plus the approximately 5 and a half million citizens in the areas they control. I don't know how many food resources are stored within the Atlanta metro area, but without resupply I suspect it wouldn't take very long to expend it all.