I think there is a very limited range of opportunity for the Germans to cause D-Day to end in disaster. Only Omaha Beach offers them this opportunity. The other beach heads made signficant headway. If the Germans attack there, the Allies could fight back effectively.
I think we can assume not all German reinforcements will be sent to Omaha, but along the entire front. While they can cause casaulties at Utah, Gold, Juno, and Sword, they will not be stopping the invasion there. They aren't going to know that Omaha is the critical spot for some time, and there will be no coordinated resistance. Rommel is still not on the battlefield.
And even at Omaha, the window is very narrow. The first troops land on the beaches there at 6:30 AM. By 10:00 AM, they are able to breach the defences and begin moving off the beach. This is the critical area of time, and I don't think German armor can affect it decisively. Allied air interdiction, paratrooper fighting, and naval gunfire is going to slow down units specifically approaching Omaha. As explained earlier, I don't think the armor approaching any other beach will have any decisive impact.
Then from 10 on, the Americans are slowly moving inland. By 1-2 PM, they are advancing and the beach is able to bring in real reinforcements. It is around this time that the German 352nd Infantry wrongly reports they have pushed the US back into the sea. By 4 PM, there is American armor arriving. Any window of opportunity has been loss at this time. Fighting ends at nightfall, and by the next day there are 9 Allied divisions ashore. Perhaps a little bit smaller beachhead, but enough that the landings are successful.
The casualties will increase on both sides, but it is very debateable whether it means the invasion must fail. It is possible it might, but I still give the Allies better than a 50/50 shot.
There will be a more difficult push in the next several days, but the Germans will suffer heavily as well.