Technically, yes. In California we can tow up to 10,000 pounds on a regular class C, what most people have. With a written test, we can get the Recreational Vehicle Endorsement (Restriction 41) to tow a fifth wheel travel trailer between 10,001 and 15,000 pounds. Above 15,000 for a fifth wheel, (or 10,000 for a bumper pull) we need a Commercial A, or Non-Commercial A.
If you were to be stopped, towing above 15,000 pounds, you would face the same type of citation as if you were driving a car without a regular license or riding a motorcycle without an M1 endorsement. Bear in mind the weights are the GVWR listed on the vehicles, not the actual weight. My SOB fiver tips the scales at 99XX pounds but is rated at 10,500 requiring me to have the fiver endorsement. By the time I buy a Cyclone I'll have my Commercial license again. I am not a driver by trade, I needed the license to be legal with the last trailer I owned.
The good news is that most LEOs have no interest in stopping RVers. If you stay reasonably close to the 55 limit your chances of getting pulled over are pretty low. Even lower are getting stopped by the officer that A. wants to cite you, B. knows you need a commercial to tow your rig and C. checks your rating sticker on the trailer. Getting stopped by a CHP commercial unit, however, is likely to result in all three being met. The most likely way to end up with an issue over licensing is after an accident.
The really good news is that with a few hours of studying, a fairly simple skills test and a drive test, you can have a Non-Commercial A and be legal. The hardest part will be finding someone with a CDL or Non-Com to drive you to the test (yes, they check).
Take a look
here.