"I hear it every day, concerns and questions: 'Is it really going to happen here?' " said Jessica Shortall, managing director of Texas Competes. Texas, she added, "will suffer an enormous price if the state projects hostility toward LGBT people."

Those on the other side of the issue argue businesses are succumbing to political correctness, making threats they often do not follow through on once the dust settles. Patrick called such concerns from the business community "nothing but bluster and bluff."

"They said all those things in Houston and we still had the Final Four," the lieutenant governor said, referring to the college basketball tournament that was held last month in the city. "The Super Bowl’s coming in January, and businesses continue to move to Houston."

Patrick announced earlier this week he is boycotting any business that "allows men to use women's bathrooms." He and other Texas Republicans have zeroed in on Target, which became the first national retailer to wade into the issue when it announced last week it will allow transgender customers to "use the restroom or fitting room facility that corresponds with their gender identity."

Shaheen said he is not worried about upsetting companies like Target, which in 2015 counted Texas among its three largest states by total sales.