John Elway is down to his last chance to identify the Broncos’ next quarterback.

If Elway can’t get it right this time, it’s time to let somebody else be general manager of the Broncos. Worse, there aren’t any obvious choices for Elway to extricate himself from this mess.

Case Keenum isn’t the answer at quarterback. He’s more Johnny Try Hard than Joe Willie Namath.

So I didn’t know whether to laugh or cry this week when Keenum declared, “I want to play here the rest of my career.”

Does anyone beside Keenum think he should be the team’s No. 1 quarterback after Sunday, when another unsatisfactory season ends against Los Angeles? That’s laughable.

With a quarterback rating of 81.4, Keenum ranks No. 30 in a 32-team league, behind Baltimore’s Joe Flacco and Jacksonville’s Blake Bortles, both regarded as QBs non grata in their unhappy football homes. A year ago, Trevor Siemian was the 29th-rated quarterback in the NFL. In other words: Elway wasted $25 million of Pat Bowlen’s money to improve the position not even one iota.

But here’s the crying shame: Getting rid of Keenum won’t be easy.

Why? While Nick Foles will probably hit the market as a free agent, it would make zero sense for Elway to have two high-priced veterans on the roster. Worse, prospects at QB in the 2019 draft class are underwhelming, at best.

With Oregon’s Justin Herbert wisely deciding to stay in school, there’s only one draft-eligible QB in college with true star quality. (Dwyane Haskins? Drew Lock? Daniel Jones? Sorry, wrong answers.)

It’s Kyler Murray of Oklahoma. While he might reconsider his baseball commitment with the Oakland A’s in order to test his mettle in NFL, Murray is smaller than Seattle quarterback Russell Wilson. Wilson’s diminutive size prevented the Broncos from drafting him in 2012, when Elway’s inability to see where the pro game was headed led to a short-sighted decision to draft Brock Osweiler.

What the Broncos have in Keenum is a bridge quarterback. But did Elway build a bridge to nowhere?

“Have I done my best? In my own mind, I could’ve done better. I should have,” said Keenum, giving a brief review of a season in which he has thrown 17 touchdown passes and 14 interceptions. “And you can say, ‘Could of, should of, would of.’ But I’ve learned from my mistakes and I’m going to continue to grind. That’s who I am.”

I appreciate Keenum’s honesty. He’s a grinder, nothing more. And there’s nothing wrong with that, so long as Keenum is content to be a quality back-up QB at a reasonable price after this inflated contract runs its course.

Elway, however, has never been a grinder. He swings big. And Elway scored big, taking a chance on Peyton Manning when nobody, including Manning, knew if he could ever throw like a Hall of Famer again.

What concerns me most about the Broncos is a football philosophy that seems stuck in the past. Elway hired Keenum, an old-school quarterback. And if Elway’s freshest idea for coach was trying to re-live 1998 with Mike Shanahan, then I’m afraid Elway might be fresh out of ideas.

The Broncos lack stability at the three most important positions in the NFL: owner, quarterback and coach.

To have any reasonable chance of winning the Super Bowl, a team needs at least two of those critical positions to be among the league’s elite.

Team ownership seems guaranteed to be messy for foreseeable future, with the Bowlen family feud likely to grow more acrimonious before order is restored.

So Elway cannot miss on his choice for the team’s next quarterback. And if Denver’s next coach isn’t a quarterback whisperer, it doesn’t matter if he’s a leader of men.

Get it wrong and it will be time for Elway to get gone.