On Monday, Brewer sounded disinclined to weaken the right to bear arms in response to the Connecticut shooting.
"I'm not sure if it's something that needs to be addressed in that respect," Brewer said, adding that a stronger behavioral health system "would probably be something that we ought to look into."
Hildy Saizow, president of Arizonans for Gun Safety, said relaxation of gun-free zones at schools and other places would be "really extremist legislation."
Instead, now is the time to support national legislation that should include toughening requirements for background checks of gun purchasers, Saizow said.
Alan Korwin, a Scottsdale author and publisher of books on gun laws, said the media is whipping public sentiment into a "mob mentality" in favor of new gun restrictions after the Connecticut shootings.
That ignores the benefits of allowing guns where they're not now allowed, he said.
Gun-free zones "enable criminals and infringe on the rights and abilities of Americans to protect themselves and their children," Korwin said. "We trust teachers with our children. Certainly they should be qualified" to have guns at schools.
An Arizona legislator who sponsored a bill after the 2011 Tucson shooting to prohibit extended magazines that hold more than 10 bullets said it would be dangerous to allow guns at schools.
"I do not see anything good of a massive arms race on our college campuses or, God forbid, on our elementary schools," said Rep. Steve Farley. "There's no good that's going to come of that."