UPDATED 08/02/12 5:40 a.m.

CHICAGO (CBS) — The culture clash over Chick-Fil-A came to a head on Wednesday, with supporters in Chicago and around the country turning out for an “appreciation day” first proposed by former Republican presidential candidate Mike Huckabee.

And Republicans in Chicago filed a formal complaint at City Hall against Ald. Proco “Joe” Moreno (1st), who wants to block the restaurant from moving into his ward because of the company’s position on gay marriage and gay rights.

LISTEN: WBBM Newsradio’s John Waelti reports

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CBS 2’s Susanna Song reports several members of the Chicago Republican Party walked into the Thompson Center, and filed a complaint with the Illinois Department of Human Rights and state Attorney General Lisa Madigan, accusing Moreno and Mayor Rahm Emanuel of breaking civil rights laws pertaining to religious freedom and the First Amendment when Moreno said Chick-Fil-A would be denied a permit.

“You could easily imagine another jurisdiction someplace in which a business owner could express a view in favor of gay marriage and have his zoning permit pulled. Would that be OK? I mean, is that fair? I mean, of course not,” said Chicago GOP vice chairman Chris Cleveland. “We are all in danger if permits someone’s permits can be pulled, and if the government can engage in economic bullying.”

The Chicago Republican Party believes it has an airtight case, based on a statute that forbids unlawful discrimination in real estate transactions – even in an oral statement.

“(Moreno) has used government power to engage in overt religious discrimination against a person who has merely expressed a sincerely-held religious belief,” Cleveland said. “Under the Illinois human rights law, that’s illegal.”

But Anthony Martinez of the gay rights group The Civil Rights Agenda said Chick-Fil-A president Dan Cathy was doing more than merely articulating personal beliefs.

“He was not expressing his religious belief. He was speaking on behalf of the company, and stating the company policy,” Martinez said.

Moreno also said last week that he is unconvinced that Chick-Fil-A will not discriminate against the LGBT community.

“If they are violating Chicago and Illinois law by discriminating against a section of our population, I think that has grounds for an irresponsible business, and that the community would not want that in there,” Moreno said.

Mayor Emanuel has also criticized Cathy’s stance against gay marriage.

“Chick-Fil-A’s values are not Chicago values,” the mayor said last week. “They’re not respectful of our residents, our neighbors, and our family members. And if you’re going to be part of the Chicago community, you should reflect the Chicago values.”

But in a statement, Mayor’s office spokeswoman Tarrah Cooper said this does not mean the mayor will be involved in trying to block the restaurant.

“If they meet all the usual requirements, then they can open their restaurant, but (Emanuel) does not believe the CEO’s values are reflective of our city,” Cooper said in a statement.

Meanwhile, nationwide as of midday Wednesday, about 613,000 people had said on Facebook that they planned to go to a Chick-Fil-A location and order something for Chick-Fil-A Appreciation Day.

At the only Chicago restaurant, long lines were outside the doors. Crowds were so large in Orland Park that cars were being diverted to another parking lot, and Chick-Fil-A kept serving those who were waiting in line even after its 10 p.m. closing time.

Huckabee, the former governor of Arkansas, said on Facebook that the purpose of the “Chick-Fil-A Appreciation Day” is to support a business that operates on Biblical values and is being targeted by “vicious hate speech and intolerant bigotry from the left.”

Huckabee said further, “Too often, those on the left make corporate statements to show support for same sex marriage, abortion, or profanity, but if Christians affirm traditional values, we’re considered homophobic, fundamentalists, hate-mongers, and intolerant.”

But gay rights advocates in Chicago are setting up an event of their own, urging people to eat at local restaurants that support gay rights.

Equality Illinois is urging Chicagoans who support gay rights to participate in an “Eat for Love Day” on Wednesday. The organization is urging people to eat at a local restaurant that supports LGBT rights and “is unafraid to show its support for equality for everyone.”

The group is asking participants to post where they are planning on eating and send pictures. Among the restaurants participating are the Chicago Diner at 3411 N. Halsted St.; Lady Gregory’s at 5260 N. Clark St.; Wilde at 3130 N. Broadway; HB Chicago at 3404 N. Halsted St.; Club Lago at 331 W. Superior St.; and the Hearty Boys restaurant at 3819 N. Broadway – which is giving 100 percent of the proceeds from its fried chicken breast sandwiches to Equality Illinois.

Another popular restaurant, Hamburger Mary’s at 5400 N. Clark St. in the Andersonville neighborhood, put out a promotion for a “hate-free” fried chicken sandwich available through the month of August. The promotion for Southern-Style Chicken Sandwich features the national chain’s mascot Hamburger Mary wearing a cow-print dress and holding a sign reading “Eat More Mary’s” with the R’s backwards – in a parody of Chick-Fil-A’s cow mascot and “Eat More Chikin” slogan.

At the Chicago location, Hamburger Mary’s is donating a portion of the sales to Equality Illinois.

Another protest is coming on Friday, when Equality Illinois is urging gay and lesbian couples to go to their local Chick-Fil-A restaurants for a “kiss-in” campaign, which the group is promoting along with other gay rights organizations nationwide.

At the “kiss-in,” Equality Illinois says, “LGBT supporters will show their disdain for Chick-Fil-A’s policies with public displays of affection in front of their restaurants.”

The controversy over Chick-Fil-A in Chicago erupted last week, when Moreno said he would be blocking Chick-Fil-A from opening its second Chicago city location in his ward, in the 2500 block of North Elston Avenue.

“I’m not going to sit on the sidelines, and allow them to come in, when I know in my heart that they believe in discriminating against gay people,” Moreno said last week.

The comments that sparked the controversy were published late last month in an article on the Christian news site Baptist Press.

Chick-Fil-A’s Cathy is quoted in the July 16 Baptist Press article: “We are very much supportive of the family — the biblical definition of the family unit. We are a family-owned business, a family-led business, and we are married to our first wives. We give God thanks for that.”

Cathy further expressed his opposition to same-sex marriage in an interview last month on the radio program “The Ken Coleman Show.”

“I think we are inviting God’s judgment on our nation when we shake our fist at Him and say ‘we know better than you as to what constitutes a marriage,’ and I pray God’s mercy on our generation that has such a prideful, arrogant attitude to think that we have the audacity to define what marriage is about,” Cathy said on the radio program.

Currently, Chick-Fil-A only has one location in the city of Chicago, at 30 E. Chicago Ave.