Stephen Ambrose often spoke about how D-day showed the superiority of democracy over dictatorship. When all the best-laid plans of D-day went to muckets, the junior officers and enlisted men improvised. The Webrmacht and Waffen SS were just as good of troops, but were hamstrung because nobody wanted to wake up Hitler. When he did awaken, he was still convinced the main invasion would be at Calais.
Even if he sent the tanks in, they would have been pulverized from the air and sea.