To state at the opening: A full out repulse was virtually impossible. Had it been even a 15% possibility the landings would not have taken place. The worst outcome for Overlord as it was designed would have been a failure on one of the beaches (likely Omaha, which was always seen as the greatest challenge) combined with the other invasion beaches getting isolated. Neither of these was likely, both were frankly impossible.
That being said...
In the end the results are the same, except the Red Army likely reaches the Rhine. As has been noted, the Western defenses would have been stripped once the Soviets reach Eastern Prussia. When that happens the Wallies go into France, either across the Channel again or into Southern France via the Med. The Allies then manage to roll across most of not all of France against fairly light resistance while the Red Army faces the mass of the Heer (pretty much as was the case IOTL).
The Soviets may be delayed in their advance on Berlin since the reserves that were used, insanely, in the Bulge are now available to defend on the Eastern front. The delay may be as much as four months, although it would likely be under three. In the end, however, the Red Army takes Berlin. Nothing, NOTHING, was going to save the Reich by mid-1944 from Stalin's revenge.
The Allies would continue, if not increase, the Bomber Offensive, with likely major increases on attacks against the rail network in Eastern Germany. Allied activity in Italy may increase as well, although that front had pretty much been discredited by spring of 1944.
It is unlikely that the Bomb is used against Germany, there were simply no worthwhile targets and it is unlikely that Germany will still be in the war in any reasonable sense by the time the weapon is ready. For the same reason the use of anthrax is vanishingly unlikely, there would simply be no reason to cross that rather broad threshold.
Probably the greatest impact in Europe is on the victims of the Camps. The Reich would have additional months to continue that senseless genocide.
The other major impact is in the Pacific. With the delay in the fall of the Reich, that means no DoW from the Soviets to act as the "other shoe" to the nuclear attacks. The chances of Olympic occuring are vastly greater in this scenario although there is also the strong possibility that the Navy & AAF gets their way and Japan is simply starved and burned into submission.
Overall, figure the failure of D-Day adds a minimum of 10 million deaths, 60-65% of them in the Pacific (where up to 1 million civilians were dying in the Japanese Zone of Occupation each month) to the WW II butcher's bill, with that figure soaring if the U.S. chooses to simply let Japan wither on the vine.