Burger King’s $1 Double Cheeseburger may be on its way out, but the financial problems left by the chain’s aggressive discounting may be tough to sweep away with a few menu changes, according to the chain’s largest franchisee.

Officials of Carrols Restaurant Group, owner of 312 Burger Kings, told stock analysts last week that Burger King has a number of new menu items ready to roll, including a breakfast muffin sandwich and a breakfast bowl. Many additions are “elevating” products priced at levels that would counterbalance the damage done to margins, check averages, and the brand’s image by the Double Cheeseburger, executives said during the call.

Yet they voiced doubts that the premium products would sell well during a time of tight consumer spending and widespread discounting. Each of the more than 300 Carrols units sold only 24 Steakhouse XT burgers per day on average after the line was added in mid-February. Those numbers were tabulated before the introductory advertising kicked in, said chief financial officer Paul Flanders. But “I’m not certain the units are going to be terribly significant,” he said.

Part of the problem, Carrols CEO Alan Vituli said, is the cheap slant the business is given by the franchisor, Burger King Corp. “BKC is coining the phrase ‘extreme affordability,’” Vituli said. As an “unforeseen consequence … that extreme affordability is converting too many of our core customers to extreme bargain seekers with no interest in looking beyond the extreme market.”

He underscored the need to “break that chain.” The $1 Double Cheeseburger generates about 10 percent of revenues for Carrols’ Burger King units, even after a slowdown in orders since December, the promotion’s second month on the menu.

“Although we are still selling a lot of Double Cheeseburgers, we have a gradual tapering off from the initial levels,” said Carrols president Dan Accordino.

The officials did not dispute that the $1 deal boosted traffic and sales after its late-October introduction. Flanders called the November increase in traffic “a dramatic improvement,” with comparable sales for that month rising 2.8 percent.

But the average check for the last quarter of 2009 fell 5.8 percent, eclipsing the 2.1 percent rise in traffic for those three months. Same-store sales fell 3 percent for the quarter.

Comparable sales have fallen more steeply since then, with an 8 percent drop for roughly the first six weeks of 2010, Flanders said.

Part of the problem, Accordino indicated, is a reluctance of Double Cheeseburger buyers to buy add-ons. Fewer drinks and sides of fries are being sold as accompaniments to the discounted sandwich.

That shift in sales patterns is also dampening profits beyond the inherent “margin degradation” of the deep discount, Accordino said.

Although officials praised Burger King Corp. for trying to counterbalance its discounting with new premium products, including ribs and the new XT burger line, they are still awaiting results.

“While we are cautiously optimistic with regard to these tactics, it is difficult to estimate the net results given the backdrop of the current consumer environment,” Accordino said.

Burger King Corp. did not respond to QSR’s requests for comment on the points raised by Carrols during the call.

Among the chain’s planned menu changes is a hike in price next quarter of the Double Cheeseburger to $1.19. Bargain hunters unwilling to spend the extra 19 cents will be offered the BK Dollar Double, a sandwich of two beef patties but only one slice of cheese, in contrast to the two provided on the higher-priced burger.

With the price hike, food costs for the Double Cheeseburger will drop below 50 percent, Vituli said.

“We’re still selling a fair amount of [Double Cheeseburgers],” said Accordino, according to a transcript provided by Seekingalpha.com.

“So the question is, when we put this [Dollar] Double burger on, will the number of units be accretive, or will we simply sell fewer Double Cheeseburgers? I don’t know yet. But I think it’s certainly a competitive strategy.”

Franchisees sued BKC in early November to reverse the system-wide $1 pricing of the Double Cheeseburger. The dissident group argued that they were losing at least 10 cents on each of the sandwiches they sold. Neither side has indicated that the litigation has been dropped since BKC disclosed its intentions of raising the burger’s price.

Carrols is not part of the group that squared off with the home office.

In addition to operating Burger King franchises, Carrols is the franchisor of two quick-service chains, Pollo Tropical and Taco Cabana.