IOTL, US defense strategy in the 50s was focused on Massive Retaliation - the threat that, in the event of a Soviet invasion of western Europe, we would conduct a massive nuclear strike on their population and industry. In the 60s, Kennedy and McNamara brought a different approach to the White House: Flexible Response, which held that the US should have a wide variety of options to respond to Soviet actions, ranging in principle from a conventional war on up. In practice, the difference was one of emphasis more than substance. But such differences are what procurement policies are made of.
So, what if the US continued to follow the Massive Retaliation strategy instead? There are a couple of ways this could be achieved - Nixon beats Kennedy, different intellectual climate at RAND, etc. This would also require butterflying the Vietnam War, obviously. At the moment, I'm leaning towards the idea that Brien McMahon doesn't get cancer in 1952, and is elected president in 1960.
"Mr. Atom" wouldn't pursue exactly the same policies as his predecessor - every president puts his own stamp on nuclear strategy - but McMahon was a proponent of the idea that a nuclear military was a cost-effective military, so he'd probably continue to emphasize strategic nuclear war-fighting rather than other capabilities.
So, assuming that this doesn't somehow lead to WW3, what does this mean for the US military, and for everyone else?