ATHENS, Ga. — It is a two-word mantra that recognizes Georgia football’s recent success and nods at the program’s history of unfulfilled hype.

“Do more.” That has been the rallying cry for this football team this season, and the scoreboard on Saturday night suggested the admonition was working.

No. 3 Georgia’s victory over Notre Dame, then No. 7, clearly moved it closer to football supremacy and left the big-talking fans of the Bulldogs aglow. But Georgia, the surest bet to win the languid Southeastern Conference East, must still outrun its own long history of showing promise but then peaking before it can get its hands on a national championship trophy.

“We understand how close we’ve been to taking the next step,” Kirby Smart, Georgia’s coach, said over the summer. “We’re not complacent in what we’ve done, and we know we need to take that next step. And for us, pressure is a reflection of ambition.”