You always have the option to communicate with the government via first-class letter delivered by the US Postal Service, or by showing up in person during the openly published hours of operation.
If the government, for some reason, decided to only communicate via telephone calls, there would still be no duty on any private phone company to provide anyone with the ability to call the government. The government would implicitly require itself to start up and operate a public telephone company, so that any person unwilling or unable to make phone calls via a private company could use it to communicate with the government instead.
In all likelihood, this would mean that VoIP phone booths would appear in every post office, and only calls from those phones to phones registered to government offices would be connected. They wouldn't even necessarily have to use phone numbers or connect to the PSTN; a .gov or .us SIP registration server would do.
For private services, if the government uses them at all, it must use them in a fair and nondiscriminatory manner. The private company has no duty to enforce this on its government users, or to police their behavior.