The 8th Circuit Court of Appeals has held that the Telephone Consumer Protection Act (not to be confused with the other TCPA) does not violate First Amendment rights to free speech. The TCPA criminalizes "send[ing] an unsolicited advertisement to a telephone facsimile machine."
The Court of Appeals concluded that fax spam imposes significant costs on recipients, and thus that regulating it serves a significant governmental interest. Further, the court held that prohibiting only commercial spam was a legitimate technique, since Congress reasonably believed that non-commerical faxes, even if unsolicited, would be more expected, and thus more welcome to recipients. Both of these holdings are consistent with results from other Circuits.
Interestingly, it seems that the Act's prohibition on telemarketing extends beyond junk faxes and cell phones to reach "any service for which the called party is charged for the call." Speaking off the cuff, I'd say this provision renders the national do-not-call list redundant. If you could get your local phone company to charge you a cent for each incoming call, presumably making it illegal for a telemarketer to call you without your opt-in permission.