Ground squirrels are indeed a pest.
Ca. Dept. Fish/Game lists the ground squirrel in a category similar to the jack rabbit. No bag limit and season is open year around.
Many areas of Ca. have been known to have ground squirrel populations with plague-like deseases. I WILL NOT EAT A GROUND SQUIRREL! Kill thousands, sure. But eat them? Never.
If you want some good laughs, use something fast and light like the 223Remington with a good varmint bullet. Don't aim for head shots, aim for the "crap factory" where all that tissue and half digested muck will let a bullet expand violently. You'll create a splat mark on the ground that is truely impressive while launching a 1/2 skinned carcass airward several feet.
The Ca. tree squirrel however is a game animal with a season from something like Sept 14 through Jan 30th. Limit is 4 per day, 4 on hand.
I just went camping this weekend hoping to get some tree squirrels and I saw 3 over the ENTIRE weekend. Was talking with some people up hunting deer and they said the Koreans came through a few weeks back on opening day and just laid waste to the area hence the reason that there were few if any to be seen(and they ran like hell every time they saw me).