I shoot a lot of panoramas, and use special heads to do it.
The short answer is that there are no cheap panorama heads.
With a lot of skill it is possible to shoot mediocre panoramas without using a tripod, by rotating yourself and you camera around the front of your lens as you shoot. This won't work if anything you are shooting is closer than 10 meters, and even then it only works 50% of the time.
There is no way around this. The lower the quality of the head, the more work you have to do on the computer. It is possible to spend as much a 100 hours working on a poorly aligned panorama. Ask yourself, is it worth it?
With the top of range (and fully calibrate) pano head, camera, and software it takes me a minimum of 10 hours to make a speherical panorama.