The beacheads themselves were garrisioned by many non-german units, such as Ukranians, and other nationalities, even Kossacks made a counter-attack on horseback!
My point is that the best troops that germany had, were not anywhere near the beaches, but what if they had been? Another Panzer Division of crack veterans could certainly made a big difference. they could have cleared one or two beachead breakouts per day. In 10 days, the allies could well have been pulling back off the beaches in a momumental defeat, especially if the luftwaffe had thrown all their reserves into it. The germans losses would have been decimating to say the least, but I believe that they could have done it.
Confusion, due to communication disruptions by the allies and the french underground played a big role in giving the allies precious time to get ashore and inland to where vital artillery could get safe emplacements. The artillery was crucial in supporting the infantry from the german counter-attacks, especialy when the bad storms struck shortly after the landings, grounding all air support for the allies.
So, if the panzers had been there to push the invaders back to the beaches, where the casualties could have been unbearable, I believe that the allies would have had no choice but to pull what troops they could off the beaches, one at a time, as the panzers showed up. such a defeat for the allies would have been catastrafic, and would most likely led to a peace accord between the combatants. Ending WWII in Europe, with the Axis holding all of europe uncontested. I believe that old Joseph Stalin would probibly eaten a bullet instead of Hitler, to avoid capture, because Russia would have been on its’ own, no peace could have been brokered between those two.
Japan too would have been on its’ own, and the USA and Great Briton would have beaten them eventually.