I would point out that even without a successful ground campaign in Normandy the Germans still had lost control over their own airspace. Allied bombers would have continued to pound German infrastructure and cities into dust around the clock. Without working railway lines, without working oil refineries, it's only a matter of time before the German economy collapses, taking with it the ability to effectively resist.
The aerial campaign does end up being somewhat harder than in reality since the airbases and radar stations in France and the Low Countries would continue to operate. But the Allies already had air superiority by June of 1944, even before the invasion.
Plus the US had the ability to move bomber forces from the Pacific theatre to Europe, e.g. the B-29 wings.
That said a failed Overlord wouldn't eliminate the possibility of a cross-Chanel invasion in 1945, before the first nuclear weapons were available. Or even the adoption of the Southern Strategy with a push through Italy. I'd be surprised if the Western Allies weren't in Europe (though not via the Frisian Islands) before the first nukes were used.
A lot of the details depend on
why Ovelord failed:
1. A working German spy ring
2. The Germans figure out their codes are broken (which has significant knock-on effects)
3. Better reconnaissance over southern England; did Hitler have a rare fit of sanity and not waste chromium and nickel on the jet bombers?
4. Was Rommel given his head?
5. Sheer dumb luck.
6. Bad weather. Historically about two weeks later a 'Storm of the Century' hit doing significant damage; did it arrive early
7. Gas. The Germans drench the beaches with mustard and nerve gases. Game over. The nukes aren't the worst that's coming Germany's way.
Operation Vegetarian.
Politics.
Don't forget the political consequences
1. A failed amphibious invasion will remind Churchill's opponents (and they were numerous) of Gallipoli; a lost vote of no confidence is quite possible after such an event. He won in July 1942 but after such a defeat?
2. 1944 was also an election year in the USA, FDR will need
some victory to survive the election, give the failure of Overlord and the lack of the liberation of Paris. Does Leyte Gulf happen as historically?
3. Then there's Stalin. He will be
loudly demanding the Western Allies do
something. It's not beyond the bounds of possibility that he restarts negotiations with Hitler. If the WA find out (was the German discovery that their codes were broken the cause for the failure of Overlord?) then the whole alliance is in jeopardy.
4. And finally let's not forget DeGaulle and the French. They're not particularly influential but they'll be unhappy at the loss of the chance to liberate France and at the elimination of the Maquis.