Try a litle vinegar on the threads are some thing to remove the lime. Can you get a socket on it, last thing is take a small hammer and chisel and tap it lightly counter clockwise, be carefull not to damage sink.
A drill with a medium bit in it will work,just drill through the nut .Sometimes you have to drill the nut in more than one place.Dont use a chisel.After you drill the nut or nuts,just grab the faucet and wiggle it back and forth and the nut should fall right off. Works for me .