score:44
If the bomb failed to explode in any way (which was unlikely, see comments and Mark's answer), the USA still would not have to worry about it (too much).
They would win the war anyway within a few months, and pick up the wrecked bomb from wherever the Japanese had stored it.
Even if Japan could figure out what that bomb was supposed to be doing and repair it, they didn't have any delivery system that could reach mainland USA (with any degree of certainty).
More importantly, the USA knew Japan did not have the capacities to build a second bomb, so even the microscopic chance that Japan could deliver the salvaged bomb to some target would not have changed the outcome.
The USA had both the delivery system and the production capacity to build a second, third, fourth bomb (of the Fat Man design), quite aside from having the strategic upper hand so firmly that they did not actually need the A-bomb to win the war. Not even in the very, very unlikely scenario of a major city, Pearl Harbor, or any other single location taken out by the salvaged Little Boy.
Upvote:-1
Adding to the above mentioned facts that the bomb would go off very easily and would be useless even after a fizzle, and that Japan was in no position to get a nuclear weapons programme off the ground, the U.S. didn't really need a contingency plan.
Japan had already started overtures for a general surrender before the bomb was dropped. The excuse the U.S. used for dropping the bomb was that they didn't like one of the conditions of the surrender, namely that the emperor would remain Japan's head of state. If the bomb hadn't gone off, the U.S. would have simply accepted Japan's surrender with the condition and leave the emperor on the throne, which the U.S. ended up doing anyway.
Upvote:43
The primary contingency plan was the design of the bomb itself. Little Boy was not a safe design: any number of unplanned events could cause a detonation. Foremost among these is impact: a 500 g impact, such as would happen after a 15,000-foot (4.5 km) fall, is sufficient to bring the bullet and target together, detonating the bomb. If the bomb hit water instead of land, the water would act as a neutron moderator, causing a criticality event and severe radioactive contamination. In the event of an airplane crash, any resulting fire will trigger the explosives, setting off the bomb.
In short, once the bomb is fully assembled, it's very hard to keep it from going off. In the event that the crew of Enola Gay had to abort their mission, they had no intention of trying to land with the bomb still aboard.