I doubt that they had the industrial resources to make one. I think the Oak Ridge facility consumed about 10% of the electrical production in the US. That's not to mention the amount of uranium ore that the US had access to.
Heck, the US even had a unit that searched for the German stores.
There is a book entitled "Alsos" which is a really good account of the U.S. intelligence effort to see how far along Germany was in building an atomic bomb.