The 18-year-old man had a fully loaded revolver inside his bag, police say.
Barack Obama entered the national spotlight with his rousing 2004 speech at the Democratic National Convention.
Little of note appears in the alleged voicemails, which NBC News hasn't been able to authenticate and isn't quoting.
Some of the strongest condemnation came from the former director of the National Security Agency and the CIA under George W. Bush.
Miami Beach police said Bradham got into an argument over how long it took for a hotel employee to bring an umbrella he and five friends had paid for.