The Idea is the US space race doesn't end but instead ramps up after the Apollo missions. Nasa gets funding about the size as a military branch and has the goals of building a moon research base, a Mars landing by the late 80s, and moving some heavy waste industry off world by the 2010s.
How would such a timeline go? How would the USSR react to this? Would the US claim the Moon as a Territory of the US once bases are built? How would THAT go over?