MADISON, Wis. — When Michael Douglas starred in “The American President” in 1995, his character joked that his approval ratings drop “5 points when Wisconsin doesn’t make it to the Rose Bowl.”

Douglas’s presidential alter ego would have welcomed this season. In its opening weeks, Wisconsin has surged to No. 8 in the rankings and emerged as the greatest hope for the Big Ten West, a division that has struggled in recent years to win conference championships. A Rose Bowl bid already seems a more than reasonable expectation for the Badgers. And by the end of October, if they can defeat No. 4 Ohio State, they may be eyeing an even grander spot in the College Football Playoff.

“You get the opportunity to play it out, and at the end there can be whatever the narrative is, but you just want your players to just make the most of each week and opportunity,” Paul Chryst, Wisconsin’s coach, said in an interview in the bowels of Camp Randall Stadium last weekend after the Badgers beat Northwestern, the reigning division champion.

Wisconsin’s rise comes as the Big Ten, filled with schools that are deservedly known as football powerhouses, faces pressure to land a spot in the playoff. The conference has been left out for two consecutive seasons and, for two years before its current run of frustration, saw its teams shut out when they reached semifinal games.