A Zogby press release reports 83% support for laws that let pretty much all law-abiding adults, at least ones age 21 and above, get licenses to carry concealed weapons. (These are generally "shall-issue" laws, because they provide that a license "shall issue," rather than just may be issued, if certain largely objective requirements for licensing are met.)
But while I support shall-issue laws, I'm pretty skeptical about the findings, because of the text of the question:
Currently, 39 states have laws that allow residents to carry firearms to protect themselves, only if they pass a background check and pay a fee to cover administrative costs. Most of those states also require applicants to have firearms safety training. Do you support or oppose this law?
The question as read over the phone obviously doesn't include the commas, so it seems to me that some listeners can easily interpret it as describing laws that limit who may carry guns — laws that "allow residents to carry firearms to protect themselves only if they pass a background check and pay a fee to cover administrative costs." The listener may well assume that these laws are enacted against a backdrop of discretionary licensing, where the police may deny licenses at will (more or less the case in California, for instance), and that the laws simply provide that such discretionary licenses may not be issued unless a background check is passed and a fee is paid.
And this is unfortunately consistent with other surveys I've seen, such as a CNN 6/4-5/08 survey that reports 48% of respondents favoring "preventing gun owners from carrying a concealed gun in public," and 52% opposing, and an ABC 4/22/07 survey that reports 42% of respondents favoring "a law requiring a nationwide ban on ... people carrying a concealed weapon (with 55% opposition). These surveys reveal at most 52%-55% support for shall-issue laws (I say at most since one can oppose a nationwide ban on concealed weapons, or even a local ban on concealed weapons, but still not support a shall-issue regime). I can't see why that would increase to 83% in the last two years; and while it's possible that highlighting the requirements of background checks, fees, and training might increase the support in some measure, I'm skeptical that the increase would be so great.
Thanks to InstaPundit for the pointer.