I don't think the Germans would get to the point that they'd even have to worry about fighting the US Army or defending thousands of miles of inland supply lines from partisans. Let's assume that the Germans and Japanese manage to (1) build up a large surface fleet, (2) draw-out and defeat the US surface fleet, and (3) build up enough merchant shipping to transport a supply a sufficient invasion force.
First, the Germans have to get those transports across the Atlantic. Even if the US lost all of its capital ships, it would still have a potent submarine fleet. Those submarines took a terrible toll on the Japanese merchant fleet, and they would have done the same in the Atlantic. The Germans will have to play the Allied role in the Battle of the Atlantic, only they'll have to do so without several key advantages:
- The Allies spent several years (and two wars) honing their convoy and anti-submarine tactics. The Germans wouldn't gain much experience in dealing with submarines until the invasion started.
- The Allies built massive numbers of anti-submarine ships and replacement transports. The Germans could too, but at the cost of either delaying the invasion or building a smaller surface fleet.
- The Allies had significant technological innovations for submarine detection. The Germans would start years behind in this field.
- The Allies had a friendly country at both ends of every transport, so patrol ships and aircraft could be based at the US and the UK instead of trying to cover the entire route. For the early stages of the invasion of North America, the Axis would have to stage everything from Europe.
Although the US submarine force could sink a lot of German shipping, some would get through. Maybe enough would make it to actually try the invasion. This is the next problem. After the fall of the UK, the Axis would have no place to degrade the USAAF. And the longer the Germans waited to build up their navy to invade, the bigger and better trained the USAAF would get. So, when the invasion started, the US could throw thousands of fighters and bombers against the Axis invasion force and its handful of carrier wings. The Germans would suffer appalling losses of troops at sea waiting to be transported ashore.
Maybe some Germans make it ashore. Now they need supplies. So the German troops capture a port, repair the damage done by the fleeing Americans, and wait for the supply ships to make it past the submarines. In the meantime, the USAAF is going to bomb the captured ports and any captured airfields. The Germans couldn't defend Wilhelmshaven from American bombers when it had locally-supplied land-based fighters. Now it will have to defend Savannah with carrier-based fighters supplied from Germany. The Germans would have trouble supplying troops to hold the beachhead, let alone a break-out force.
With all of that said, if the US had been run by the HOI3 AI, it probably would have been pretty easy.