Meanwhile, the owner of the Dallas Cowboys, Jerry Jones, is trying to block an extension of Mr. Goodell’s contract. The commissioner’s current deal expires at the end of the 2018 season. NFL insiders originally expected the deal to be extended this past summer. Mr. Jones, who owns more than 100 Papa John’s franchises in Texas, has reportedly been rallying support among fellow owners to oust Mr. Goodell.

Asked Friday about Mr. Schnatter’s rebuke of the commissioner, Mr. Jones hailed the pizza tycoon as a “great American.” Speaking on a radio show Tuesday, he was even more explicit about Mr. Goodell: “I know a lot of people, a lot of fans, don’t think we make him as accountable as we should,” Mr. Jones said. “But that’s not the case. It’s just timing. When you have to account is when you’re either getting hired or you’re getting extended or you’re getting a raise or are you getting a bonus.”

In other words, the time for action has arrived—and Mr. Goodell has a lot to account for. Concern over head injuries has eroded football’s public support. Mr. Goodell’s handling of player discipline, particularly the 2014 Ray Rice domestic-violence case and the 2015 New England Patriots “Deflategate” scandal, damaged the NFL’s image. Now unending national-anthem protests have frustrated the league’s conservative fans, made it a target for President Trump, and contributed to sliding TV ratings.

It makes sense to blame ineffective leadership. But what if the problem is effectiveleadership? Football is headed exactly where Mr. Goodell has steered it—to the left. The NFL has long been a combatant in America’s larger culture war. But Mr. Goodell—whose father, Charles, was a liberal antiwar Republican senator in the late 1960s—was always an odd choice to run it.

Remember that the NFL was cultivated into prominence by Pete Rozelle, a pro-war conservative. In the 1960s, Rozelle hired a World War II veteran-turned-filmmaker, Ed Sabol, to produce highlights, commercials and documentaries that marketed the sport as patriotic and militaristic. Sabol’s NFL Films made football feel more American than baseball. His work was so critical to the league’s wild growth that in 2011 he was inducted into the Pro Football Hall of Fame. The same honor had been bestowed on Rozelle in 1985, while he was still commissioner.

By contrast, a year ago Mr. Goodell hired a Democratic political strategist, Joe Lockhart, as the NFL’s executive vice president of communications. Mr. Lockhart, best known as President Clinton’s press secretary for two years, also worked for Jimmy Carter, Walter Mondale, Michael Dukakis and John Kerry. Last week the New York Times credited him with crafting the NFL’s message on the anthem controversy.

Mr. Lockhart is an aggressive media manipulator. The Times reported that several NFL owners were bothered by a snide comment Mr. Lockhart made about Mr. Trump: “Lockhart told reporters that talking about police brutality is ‘what real locker room talk is.’ ”

But Messrs. Goodell and Lockhart have made bigger gaffes. In mid-October, Mr. Goodell and Seattle Seahawks wide receiver Doug Baldwin wrote a letter to the Senate “to offer the National Football League’s full support for the Sentencing Reform and Corrections Act of 2017.” Mr. Goodell is paid $44 million a year to represent the views of the NFL’s owners, not players or himself.

An ESPN story in late October about the anthem protests portrayed Mr. Goodell as supporting players’ desire to use the NFL as a platform to address whatever social issues they deem important. Buried deep in the article was an anecdote about the owner of the Houston Texans, Bob McNair, complaining to fellow owners, Mr. Goodell and a handful of NFL executives that “we can’t have the inmates running the prison.” Texans players took offense and staged an anthem protest before their Oct. 29 game against the Seahawks.

Mr. McNair apologized but said he was misunderstood. “I was referring to the relationship between the league office and team owners,” he said in a written statement, “and how they have been making significant strategic decisions affecting our league without adequate input from ownership over the past few years.”

Messrs. Goodell and Lockhart are damaging the league’s longstanding and highly profitable brand. Neither one seems likely to join Pete Rozelle and Ed Sabol in the hall of fame. The question is how long the owners will continue to allow the pair to reshape the NFL.

Mr. Whitlock is a co-host of “Speak for Yourself” on Fox Sports 1.