That said, yes, if we pit say 10 German armored divisions and 40 infantry divisions against what the Allies had landed by D-Day +10, onto an ideal, open, limitless battlefield surrounded by vacuum, the Germans would win. But that's not what would have happened. The battle wouldn't be fought in a vacuum.[/FONT]
For starters, the German reinforcements would have to be shipped West. And, not coincidentally, the French rail network was in shambles, the German one not much better off, and both still under Allied strategic bombing attack. The situation was bad enough with the reinforcements the Germans actually sent in OTL, increase them, and you won't have more German troops on the frontline; you'll have more German troops on sidings and marshalling yards from Smolensk to Paris, waiting for rolling stock the Germans did not have. And while there, they'd be bombed together with the rail lines.
Of course, the same goes for the supplies these units would need. It's no good to have Koenigstigers around if you aren't getting fuel and spare parts for them.
Once the units reach the vicinity of the frontline, already whittled down by these problems, there's the Western Allied tactical airfleet, which had not a lot to do in OTL due to a shortage of suitable targets. In this ATL, they get what they'd call a "target-rich environment".
And once the survivors get close to the shores – naval bombardment. For a few hours in each case, the Germans had thought they had half a chance both at Gela and Anzio the year before; the battleships' guns melted that half chance.
So in the very best case the Germans can contain the landing, for longer than they did historically, and at an accordingly much higher price. But I very much doubt they'll be able to do away with it.