Quite well, actually. States with "shall issue"[1] laws have seen a significant reduction in violent crimes. I believe Florida is the one with the longest data.

Much like the repeal of the national 55mph speed limit, the arguments against were all FUD. Neither resulted in bloodbaths.

[1] A law which requires the state to issue a permit to carry a concealed weapon, except under specific disqualifying circumstances, which the state bears the onus showing.