Sanchez and Tebow are part of an N.F.L. tradition about as old as training camp. A quarterback duel wouldn’t seem to be a recipe for success for a team that missed the playoffs last season and appears to have lost its ability to roar.

“John Madden used to always say if you have two, you don’t have one,” said Rich Gannon, who played in the league for 18 years and was a most valuable player and a Super Bowl quarterback for the Oakland Raiders. “I think there’s some truth to that.”

Asked about the Tebow-Sanchez situation, Gannon said it had the makings of a collision.

“I just think it’s going to be hard to manage the expectations all season,” said Gannon, now an analyst for CBS and SiriusXM NFL Radio. “Tim Tebow is such a polarizing figure — I say that in a good way. He’s one of the most popular players in the league, even though he’s never been to a championship or been to a Pro Bowl. He’s a guy who gets a lot of attention; there’s a lot of curiosity around him.”

We won’t have to wait long for discontent to surface.

“The minute Sanchez struggles there’s going to be: ‘Why not Tebow? Why isn’t Tebow playing more?’ ” Gannon said. “It’s going to be a story every week that’s going to be the balancing act the Jets are going to have to deal with the entire season. No fault of Tim Tebow’s. That’s just the way it is.”

There have been notable quarterback controversies in the N.F.L. over the years: Drew Bledsoe and Tom Brady in New England; Troy Aikman and Steve Walsh in Dallas; Jay Schroeder and Doug Williams in Washington; Doug Flutie and Rob Johnson in Buffalo; Phil Simms and Jeff Hostetler with the Giants; Joe Montana and Steve Young in San Francisco.