I don't see how it could. The U.S. Government has no one to ask for backdoor access to bitcoin. One of the many benefits of decentralized organization.

However, there's certainly secondary and tertiary affects. The government can already get your email with warrants and other compulsory legal processes for other kinds of data: so if you're sending your private keys with nothing more than your email service's encryption, yeah you're screwed if the government wants to eventually seize your Bitcoin pursuant to valid civil or criminal forfeiture order.