This would mean that "pre-emptive" strike is suddenly lot sweeter deal for U.S. Alternatively restart midgetman program. Yay, more nukes. https://en.wikipedia.org/wiki/MGM-134_Midgetman
This would be "destabilizing" technology. I hope it goes nowhere.
It's obviously not as applicable to a ballistic launch, but here's an example of publicly known missile guidance that doesn't care about satellites:
https://en.wikipedia.org/wiki/TERCOM
I expect even without improvements like that they are prepared to launch and hope that the inertial navigation system in the missile is good enough.
TERCOM is very nice, but only applicable for cruise missiles flying close to ground and able to change their course.
The more important point is the question of whether GPS is actually required for a launch or if it merely improves the process (accuracy, speed, etc).
While GPS might be used to refine locations, both subs and their missiles use inertial navigation that isn't dependent on satellite clusters. A long term lack of GPS would hurt accuracy, but a Russian attack on the GPS system would be such a provocative act that its direct long-term effects on targeting and navigation would probably be insignificant compared to the indirect long-term effects by way of the broader conflict it provokes.
But anyhow just the capability to kill satellites would mean increased tension between the nuclear superpowers.
The US demonstrated that capability in 1963, the USSR in 1978.
Mandatory Simpsons gif: https://media.giphy.com/media/axMy0g9z9khZC/giphy.gif
Since by definition the US missile sub fleet would be used for a second strike role in this situation (by definition, since someone else nuked the satellites first), the strikes would primarily be retaliatory in nature - ie, nuke the cities. Big whoop if your CEP is now 500m when you're nuking Moscow.
Though Russian missile subs worked without such positioning, so they would probably still mean business.