They won’t be brandished as a supply chain risk because the supply chain members are good at lobbying and they like Claude.
As an example, Amazon is a defense contractor and uses Claude heavily internally for development. They are also major investors in Anthropic. Amazon would not want Claude to be banned from use on developing AWS services that may be cross sold to the government. Multiply this by every defense company that uses Claude (eg anduril and Palantir).
They could totally try and punish Anthropic executives of course. That seems likely.