There isn't anybody that "novocaine" -- usually lidocaine or xylocaine -- doesn't work on. If it "doesn't work" the guy injecting it is not using enough or in the right area which is actually not that uncommon among many doc's. Local anesthetic are really miracle drugs. Hence, go to somebody well-practiced and patient. Generally (not always) a general surgeon would be a better bet. Generally of course, not in every instance.
Actually, actual Novocain is chemically an ester and there are cholesterases in the blood such that it can render the drug (and any local anesthetic that is an ester) ineffectual as an anesthetic. Lidocaine, bupivocaine and the like are chemically amides and are unaffected by blood.
I can only speak from my own personal experience from dental and local surgeries (such as my vasectomy) that while the local anesthetics do work on me, it's just that I need a larger dose and longer time for it to take effect.
My dentist has finally figured it out after the few times I've planked on him while getting a filling. Now he hits me twice and waits about about 30 minutes before he starts to work.
Was the same thing with the vasectomy. The doc injected both sides. The first one was pretty sensitive. He hit the second side again before doing it and I didn't feel a thing.
