An interesting hypothetical question. To assume the Germans were not deceived to the full extent by Operation Fortitude, but to still allow the Allies some realistic security maintenance as would accompany almost any large offensive, one could argue that the Germans could have defeated the landings if they had placed their mobile forces in the optimum locations.

The essence of the Allies' success was in their getting their units ashore on the day without having to face any serious resistance from the various Panzer and SS Panzer divisions Hitler had positioned in France to resist the invasion. The management of these was the subject of controversy among the German leadership and led to a convoluted command structure that compromised the defence, but given the overall success of Fortitude in making the Germans prepare for another landing in Calais, whether their tanks were positioned close to the beaches, or inland, was probably moot: in the event the Allies were able to build up their defence and establish a viable perimeter before the German tanks arrived in force.

You are right the Germans faced the invasion with many handicaps: the principal one being the almost complete destruction of their air power, the destruction of their transport networks and the paucity of their equipment. But against this, a major opposed amphibious landing is perhaps the most difficult of military operations and it would take many days for the Allies to build up a force capable of resisting a majority of the armoured forces the Germans had available, even given Allied air superiority. In the first days the bridgehead was delicate indeed, and much of the delay in securing objectives, such as the reversal in the morning at Omaha or the failure to press on to Caen, was the result of resistance by small units and in some cases individual strongpoints.

Once the battle of Normandy began in earnest, the Allied trump card was often artillery, a mass of which was on hand to stop German infantry or armoured attacks. To deploy all this artillery needed space and time, and to resist such attacks required depth.

One can make an excellent case that had Rommel been able to position the 1st SS, 2nd SS, and 12SS Panzer divisions close to the invasion beaches the landings could have faced defeat. He had several other Panzer Divisons available as well. The Allies knew delaying them was crucial and this was the main objective of their deception plans. But once ashore, over for just a week, even an attack by the full mass of these units could probably have been held.

Sources: Six Armies In Normandy John Keegan; Gold Beach: Jig Tim Saunders; D-Day: Spearhead of Invasion R.W Thompson; Das Reich Max Hastings; The Secrets of D-Day Gilles Perrault; A Bodyguard of Lies Anthony Brown.