[giantrobot]

Heat shields are not trivial but they're achievable with 1950s era technology. If you pay the mass penalty you can just use a big "dumb" ablative heat shield. With a bomb you don't need to build anything too sophisticated, it only needs to work once and you don't want it back.

With a rocket capable of getting a meaningful payload to LEO you've got the power to pay that mass penalty if the trajectory is ballistic.

None of this is "easy" but it comes along with developing orbital capabilities. This is why Sputnik's launch was such a big deal to defense planners. If the Soviet Union could get a little satellite into a stable LEO it could deliver a warhead to the continental US.