Could the Germans have won on D-Day?

 Yes, there was certainly a chance that the D-Day landings could have been defeated. The Germans knew the landings were coming and worked hard to strengthen the 'Atlantic Wall' to stop them. The weather was uncertain—the original planned date was June 5, and many troops had boarded their ships in preparation for that day, only to be delayed due to bad weather. Eisenhower received a favorable weather forecast from Ireland and decided to proceed on June 6, but it was still a risky decision. Rommel believed the Allies would not invade under such conditions and took the opportunity to visit his wife in Germany. If the weather had been worse and Rommel had been present, the Germans might have been able to repel the landings. There was a precedent for this: they had successfully defeated Operation Jubilee, a major landing at the port of Dieppe in August 1942. This is a German photo of the aftermath:

Eisenhower fully understood the risks of Operation Overlord. In case the landings failed, he even prepared a statement taking full responsibility:

"Our landings in the Cherbourg-Havre area have failed to secure a satisfactory foothold, and I have withdrawn the troops. My decision to attack at this time and place was based on the best information available. The troops, air force, and Navy did all that bravery and dedication could do. If any blame or fault lies with the attempt, it is mine alone."

Several factors contributed to the success of Overlord: lessons learned from earlier landings in North Africa, Sicily, and Italy; the use of deception, which convinced the Germans that the main attack would happen elsewhere; Allied air superiority (Rommel, a key German commander, was badly injured by Allied aircraft on July 17); and help from the French Resistance. Even so, amphibious landings are among the toughest military operations, and, as later battles at Caen and Arnhem showed, the Allies didn’t always have luck on their side.

D-Day could have failed. If it had, the war would have dragged on longer. This might have allowed Germany to strengthen its position on the Eastern Front or negotiate peace with the Soviet Union. Alternatively, the Soviet Union might have ended up occupying all of Germany. It's impossible to know for sure, but Operation Overlord had no guarantees of success.