Flight Crew Air Transport Pilot (ATP)
Flying north with Miami Center southeast of CRG. [There were] significant buildups and moderate turbulence throughout the area. [There were] many aircraft on frequency trying to check-in and trying to get clearances to avoid weather and turbulence. The Controller was doing her best to handle the radio traffic; but; as she stated; she was working two frequencies simultaneously. Therefore; it was difficult to contact her as everyone was stepping on everyone else's transmission; she wasn't receiving our calls; and her calls were being blocked. This was a weekend afternoon; so I don't know if ATC is minimally-manned during this period; but the working Controller was doing the best she could; but she was nevertheless overwhelmed by the circumstances. In my opinion; she needed to be working a single frequency and; frankly; that would have been very busy. This report is in no way suggesting the Controller was faulty or making mistakes. As noted above; she was doing an admirable job in a very tough situation. The density of aircraft coupled with the bad weather situation really required additional Controller availability. Fortunately; we didn't need to declare an emergency to avoid weather (due to an inability to communicate with ATC) and didn't come close to another aircraft. But; the potential for both was there. Storm buildups; turbulence; and aircraft density should require ATC to work a single frequency in order to allow for clear and frequent communication.
Pilot reports Controller working two frequencies and can't contact the Controller due to congestion on the frequencies.