It could depend on where a nuke or nukes detonates, and how much damage it causes. If a substantial part of New York or Washington is destroyed, then the retaliation would likely be on a much larger scale than if it was, for example, a medium-sized port city that is not a financial or governmental or media hub.
Trashing "half the world" would only bring down the entire post-WWII world order that Washington has dominated for over 60 years, so why do that. Washington often acts irrationally, but also has a keen sense when it comes to preserving its own power and prerogatives.
The one thing that would occur for sure is the complete militarization of U.S. society. Whether or not that can besuccessfully accomplishedin a balkanized, decadent land such as this is another question altogether. More likely, it would work some places but not others. The non-white cities would move closer to "warlord" status, while white rural areas would become more independent from Washington's dictates.