I'm sure Alex Karp and Palantir are already charging into the breach, promising to deliver things they don't have the capability to deliver! (Otherwise known as just another day for them)
I would think it pretty clear that they aren't shy about making their displeasure loudly and concretely known when denied. I can imagine an executive order in the research or draft state that'll make it so any entity that continues to deal with Anthropic is automatically put at a disadvantage. Something similar in spirit and effect to the sanctions on Cuba.