According to this book, in May 1949 (months before the Soviet's first bomb test), the US had 133 nuclear bombs and a plan (in case of war) to bomb 70 Soviet cities, but concluded that this was probably insufficient to "bring about capitulation". The book also mentions that the US panicked and speeded up the production of nuclear bombs after the Soviet bomb test, so if it had done that earlier, perhaps it would have had enough bombs to deter the Soviets from developing them.

Also, according to this article, the idea of using nuclear weapons to deter the development/testing of fusion weapons was actually proposed, by I I Rabi and Enrico Fermi:

They believed that any nation that violated such a prohibition would have to test a prototype weapon; this would be detected by the US and retaliation using the world’s largest stock of atomic bombs should follow. Their proposal gained no traction.