NEW YORK  — Competition among casual restaurant operators heated up Tuesday, as Denny’s Corp. launched free Grand Slam breakfasts in an effort to reacquaint customers with its brand and showcase its meals as value-friendly options for cash-conscious consumers.

The restaurant chain gave away the free Grand Slams, which include pancakes, eggs, bacon strips and sausage links, to any customer visiting its restaurants on Tuesday between 6 a.m. and 2 p.m.

Denny’s has promoted the freebie heavily, with a 30-second ad that aired during the third quarter of the Super Bowl on Sunday, another 15-second ad during the post-game show and a full page ad in USA Today’s Monday editions. The company reported 14 million hits on its Web site between Sunday night and Monday morning — the site read “service unavailable” at midday Tuesday.

With the promotion only under way a few hours, spokeswoman Cori Rice said restaurants in Miami, Washington, D.C., and Los Angeles were reporting long lines and other locations said they were very busy but under control.

“From all reports, it’s going extremely well,” Rice said.

The Spartanburg, S.C.-based company anticipates up to 2 million people will take advantage of the deal, with Rice saying each restaurant will be able to churn out about 100 Grand Slams an hour.

Denny’s, which has more than 1,500 locations, sells more than 12.5 million Grand Slam breakfasts a year.