There are several ways that the US could launch satellites even with how degraded their capabilities are - the question is more do they have anything to put on top of the rockets not do they have the rockets.

For one it would be relatively easy to launch to low orbit using an air launch with a B-52 as the mother craft or similar aircraft. Also any surviving ICBM's (and based on the low use of those weapons there would be a bunch around) could easily be used as launch platforms

Could they put together some very low tech satellites - i.e. basically recreate the original early 1960's models - probably - but the question is with all the debris in low orbit would they be able to safely orbit one - especially without worldwide radar coverage and controllers to help any satellite to maneuver to dodge debris

Jodrell Bank actually was the early warning radar for the West until the BMEWS balls in Yorkshire were built.

I would recommend that those of us interested in this concept read Dale Brown's Dreamland series -- the military uses the aircraft of a contractor named John Masters to deploy what they call NIRTSATs -- Need It Right This Second sATellites.