Boston Mayor Thomas Menino and Chicago Alderman Proco "Joe" Moreno have both said they will try to stop the chain from opening more outlets in those cities, The Atlanta Journal-Constitution reported.
"Chick-fil-A is part of the South. It's part of the Southern culture, and they've done an outstanding job of expanding over the years," Greg Sanders, publisher of Food News Media Group, said. "But let's be frank, if they're new in California, not only are social attitudes possibly different in that part of the country, but there's also not a bank of good will with that brand being built up for years in the South."
The privately held chain began with a chicken restaurant, the Dwarf House, opened by Cathy's father in an Atlanta suburb in 1946. Chick-fil-A originally targeted shopping malls and now has nearly 2,000 restaurants in 39 states.
The family is devoutly Christian and Chick-fil-A outlets are known for closing on Sundays.
Cathy's remarks about traditional marriage, which also opposed divorce, have brought him both fierce opposition and support. Former Arkansas Gov. Mike Huckabee declared next Wednesday "Chick-fil-A Day" on his television show while some gay groups have urged gay couples to select Chick-fil-A outlets for "National Same-Sex Kiss Day" next week.
There have also been calls for boycotts.
Peter Saleh, a restaurant analyst with the Telsey Advisory Group, said the controversy could hurt the chain's profits for a while.
"We've seen other PR nightmares or PR issues with companies and they will bounce back," he said. "It will just take some time. Maybe a couple of quarters."