Tom,
I'll take a stab at it. I'm an extra-class ham (wb5tht) and know a little about antenna matching.
First a little background..
To simplify things, all antennas not a multiple of some wavelength (1/4, 1/2, 1/1, etc) at a particluar frequency will not "accept" the waveform produced by the transmitter. Waves will be reflected back to the transmitter and only a small portion of the energy will actually be radiated from the antenna.
CB is at about 27 Mhz which is about 102" at 1/4 wavelength. Nobody wants a 102" whip on top of their coach, so what to do? The answer is adding inductance and capacitance at the antenna to "fake out" the transmitter so it will in this case send about 4 watts or so out the coax towards the antenna.
Not all of the power will actually be radiated out of the antenna - some will absorbed by the matching device at the base of the antenna.
So what does that mean in my case you may ask? It is very difficult to remotely troubleshoot your problem. An investment in a good swr analyzer of meter would be a good thing. You could be the hit of the campground if others find out your testing abilities. An excellent source of ham products is MFJ -
http://www.mfjenterprises.com/index.php.
I would not trust the built in swr meter unless you know for a fact it works. Perhaps you can try the radio in another location with a known good antenna. Your antenna's matching network could be defective. If the antenna is mounted on fiberglas and not specifically engineered for that installation, you might not ever get a decent swr (decent= less than 1.5 to 1).
As an aside, the "shortie" antennas for CB will never ever be as effective as a 102" whip - they are all compromises in favor of size. Something else I thought of is to not have any other metal objects near the antenna as this will detune the antenna (like mounting a 102" whip on the back bumper.) The space around the antenna should be clear of objects for at least two or three feet.
Sorry to be so long with the post but maybe it will help your troubleshooting if you understand some of the dynamics involved. Some of the theory is a gross oversimplification - forgive me my fellow hams and EEs reading this post ;-)
Let me know if you have any questions.
John
www.janeandjohn.org