ATLANTA — Delta Air Lines, one of Georgia’s largest private-sector employers, is among the glossiest corporate jewels in the state, contributing an estimated $435 billion a year to the economy with its hundreds of daily flights in and out of Atlanta’s airport.

“Delta is the Atlanta international airport, and our airport is, you know, the fuel that generates our commercial community,” said Sam Massell, the city’s former mayor.

But in the wake of the Florida school shooting, the airline announced it was ending a promotional discount with the National Rifle Association, and suddenly found itself in the rare position of being openly dressed down — and potentially punished — by Republicans who control the statehouse.

Lt. Gov. Casey Cagle of Georgia, a Republican who presides over the state Senate, joined other conservative lawmakers this week in threatening to remove a $50 million sales tax exemption on jet fuel that some hoped would encourage Delta to open even more routes.

The conservative backlash highlighted the challenge confronting corporations around the country amid an incendiary national debate over gun control.

As pressure from social media and advocacy groups has intensified, and calls for boycotts mount, more than a dozen companies have severed business ties with the NRA. Just as quickly, a counteroffensive arose from gun supporters excoriating the companies for their stance.

Delta did not respond Tuesday to Cagle’s threat or amplify its stance regarding the NRA. In a statement over the weekend, the company said its decision to stop offering discounted fares to the NRA “reflects the airline’s neutral status in the current national debate over gun control amid recent school shootings.”

As of Tuesday afternoon, the jet-fuel tax break, while opposed by Cagle and some other conservative Republicans, had not yet been stripped out of a broader Senate tax bill.

State Sen. Josh McKoon said in an interview Tuesday that he was put off by Delta’s assertion that it was trying to remain neutral on the guns issue, when it had taken positions on other social topics in the past.

But Massell, the former mayor, called the entire debate “embarrassing.”