The odds of being extradited are slim, but it won't mean the warrant will go away. The California DMV can also put a hold on your license and you may not be able to get a drivers license in your home state.
Try to figure out a way to deal with it. An attorney in the jurisdiction where the case is should be able to get the warrant recalled without you having to fly back.
Very slim chance of extradition request from Il for a misdemeanor. However, this may end up, now or when you attempt to renew your CA license, putting a hold on your license until you resolve the DUI. I have had people forced to come back to Il for decades-old unresolved DUI charges.
It is always possible but highly unlikely. The real issue that you will have to face in the future is issues with getting a valid driver’s license as a suspension in one state will cause suspensions in other states.
I agree with the above attorneys that extradition from Illinois to California is very unlikely. However, it is VERY likely that the State of Illinois will discretionarily revoke your driver's license. You would need a hearing at the Illinois DMV to reinstate....also, the CA warrant would remain outstanding until dealt with in CA.