Buy a handle puller and when you re-installl use a little faucet lube, which you should have done in the first place.

You need a handle puller. Once you get the handles up, you probably still have to remove the bodies under them. try unscrewing with both hands, or use a small strap wrench.

This post was edited by homebound on Sat, Oct 12, 13 at 22:23

Thanks. I see how the handle puller will work for the lavatory handles but not for the single handle kitchen faucet. The center shaft would have to go right into the handle. Do they make a different kind for that or is there some other trick ? I thought of fitting a wood brace under it and tapping the brace with a hammer.

Since any repairs or adjustments require that the handle be removed, remove the set screw and, repeatedly, apply your chemicals, CLR, vinegar or lime away, into that space.
Attempt to move the handle in s motion adverse to its normal motion.

If all else fails, be prepared to sacrifice the handle.