Tennessee Gov. Bill Haslam has a vastly different message about the new tax law than some of his fellow governors up North, and it can be summarized in three words: Bring it on.

The Republican, who is serving his second term as governor, says the old code advantaged residents in high-tax states because it allowed them to deduct an unlimited number of state and local taxes from federal ones.

“That’s not going to be true anymore,” Mr. Haslam said in an interview. “We governments have a price just like a business does. And, by the way, customers get to choose where they do business.”

Southern states, where economic growth is outpacing Northern counterparts, are predicting that a new $10,000 cap on the federal deductions taxpayers can take for state and local taxes will make low-tax states more attractive for workers and businesses.

The South’s optimism contrasts with worries in many Northern states that the changes will hurt their economies, where higher state and local taxes were offset, in part, by federal deductions for decades. New York Gov. Andrew Cuomo, a Democrat, said earlier this month he would sue the federal government for the tax changes, which he described as “an arrow aimed at New York’s economic heart.”