Let us suppose that the Soviet Union, for a POD of your preference (Sergei Korolev does not die? Vasily Mishin is not chosen as his successor? The URSS take the Space race more seriously from the beginning? Choose the one you like more) manages to beat the United States to the moon, forever depriving the United States of their "iconic" victory. Bonus point of the Soviet Moon Landing take place on 4th of July.
What would the reactions have been?
How would the American people, Congress, Nixon and NASA react to this new defeat?
And how could the other nations of the world react?