It's probably not the compressor.
I have a 6HP compressor as well,just with a bigger 60 Gallon tank,which runs our entire shop. The compressor size isn't really that important for taking off lug nuts,as long as you have more than 100 psi or so. A bigger compressor and bigger tank is only needed for longer continuos duty. You may find that with your smaller compressor,you may have to stop and let it fill back up after taking off a wheel,before continuing on to the next.
Your problem is most likely a flow restriction,such as fittings,dryers,or the hose itself. You should have at least 1/2" supply lines to where you are working,as short as possible,and then a short 3/8" line to the gun itself.
If you have an air dryer,lubricator or pressure regulator then they may also be the cause of the restriction. A lot of the cheaper ones are only 1\4" ID and will severly affect airtool performance. You should also avoid using any 90 degree fittings in your installation as they also will reduce performance. Cheap quick couplers may also have very small internal diameters as well. Keep the whole setup as short as possible.
Try using just a short piece of good 3\8 hose directly from the compressor to your gun,and see how it works. If you now have lots of power,then you will have to figure out what is causing your restriction,and rework your air supply accordingly.
If you don't have a pressure gauge,then get one. Your cutout switch on the compressor may be set to low and you may not have enough pressure in the tank. Most are adjustable,usually 120-125 PSI is a good balance between airtool performance and compressor life.