Target is facing a nationwide backlash for its support of transgender rights.

More than 1.2 million people have signed a pledge to boycott the retailer after it announced last month that it would welcome transgender customers to use any bathroom or fitting room that matches their gender identity.

Critics have been holding protests and demonstrations at stores across the country, and they are showing no signs of dying down.

Many are demanding access to bathrooms of the opposite sex to support claims that "perverts" can now prey on children and women as a result of the policy.

The boycotters' goal is to force Target to reverse its policy, or at least make the retailer suffer for it by spending their money elsewhere.

But Target CEO Brian Cornell dug in his heels on the issue this week, saying Target won't reverse its stance.

"We took a stance and we are going to continue to embrace our belief of diversity and inclusion," Cornell said on CNBC.

So what does that mean for Target's business?

Sales may drop for at least short period, according to YouGov BrandIndex, a firm that measures consumer perceptions of major brands on a daily basis.

Before the boycott, 42% of consumers considered buying from Target the next time they shop at a department store. In the last couple weeks, that share has fallen to 36%, according to YouGov data provided to Business Insider.

Consumer perception of the brand has also dropped sharply. It's at its lowest point in two years.

Despite the drop, Target is still in "positive" perception territory. In other words, there are still more people who think positively about Target than negatively.

"There's a very large group out there that supports Target's decision," says crisis-management expert Kevin Dinino, CEO of San Diego-based KCD PR.

He pointed out that nearly 80 million people shop at Target's stores every month, so "at worst, we are talking about a group of 1.2 million shoppers — or 1.5% of Target's customers — who are disenfranchised."

Investors also don't seem too concerned about a long-term sales impact.

Target's share price has lost 9% of its value in the last month, but it's up 3% so far this year.

In the past, even the most widespread calls for company boycotts have tended to blow over within a matter of weeks to months.

Chick-fil-A, for example, faced a nationwide boycott in 2012 after Dan Cathy, the son of the late Chick-fil-A founder S. Truett Cathy, set off a fury among gay-rights supporters when he told the Baptist Press that the company was "guilty as charged" for backing "the biblical definition of a family." Following Cathy's remarks, reports emerged detailing Chick-fil-A's many charitable donations to anti-gay-marriage organizations.

Despite the backlash, Chick-fil-A's sales soared 14% in 2012.

Ultimately, access to goods will outweigh moral outrage for many consumers, says Larry Chiagouris, a professor of marketing at Pace University’s Lubin School of Business in New York.

"The boycott is not going to last very long," Chiagouris told Business Insider. "There is a big difference between signing a petition compared to not taking advantage of a big sale at target. People will always take advantage of the sale."