The NFL’s worst nightmare is suddenly at its doorstep: the Kansas City Chiefs, the league’s most reliable postseason attraction, are in real danger of missing the playoffs.

They enter a showdown against the Los Angeles Chargers at Arrowhead Stadium on Sunday, needing a victory to extend their slim hopes of making an 11th consecutive post season appearance, a stretch that has included five Super Bowl appearances and three Lombardi Trophies.

Their era of dominance is in peril thanks to a meager 6-7 record. The Chiefs need to win their remaining four regular-season games and hope other contending teams lose several games to avoid their first playoff absence since Patrick Mahomes became the starting quarterback.

“We’re in unprecedented territory,” Mr. Mahomes told reporters in Kansas City. “We’re in a place where we haven’t been since I’ve been here. At the end of the day, we have to handle our business first. We have to win football games and let the rest handle itself.”

The problem is the Chiefs haven’t been winning. They’ve lost four of their last five games, are under .500 in December for the first time since 2012 and saw their nine-year streak of AFC West titles end with a 20-10 loss at Houston last Sunday.

Expecting them to run the table is challenging. The Chiefs will be favored to defeat the Tennessee Titans (2-11) on Dec. 21 and the Las Vegas Raiders (2-11) in the regular season finale. But difficult games loom against the Chargers (9-4) and the division-leading Denver Broncos (11-2) on Christmas Day.

Winning all four games may not be enough as the Texans (8-5), Buffalo Bills (9-4) and Jacksonville Jaguars (9-4) hold head-to-head tiebreakers over the Chiefs, who also hold the worst conference record of any of the top AFC playoff contenders. The situation is so dire, according to NFL research, the Chiefs have an 11% of making the playoffs. A loss on Sunday would drop their playoff probability to less than 1%

“I don’t know what the percentages are, but I know they’re not high,” Mr. Mahomes said. “I think it’d be special if we get into the playoffs and make a run.”

The NFL wouldn’t mind a miracle. The Chiefs’ consistent success has made them a team that many fans either love or hate but must watch. High-profile personalities like Mr. Mahomes, tight end Travis Kelce and head coach Andy Ried have made them a fixture for prime-time and holiday games. Kansas City’s matchup with the Dallas Cowboys on Thanksgiving Day, averaged 57.23 million viewers on CBS, making it the most watched regular-season game in the history of the NFL.

But the Chiefs won’t be on television past the regular season if they don’t get an improved performance from Mr. Kelce and others. The former All-Pro tight end and fiancé to pop star Taylor Swift had two crucial drops against the Texans, including one that led to a game-deciding interception.

“I feel like I’ve always had the answers in years past, and this year I just can’t find them,” Mr. Kelce said on his New Heights Podcast. “I keep think if I show up to work and I put in the work and I fix the issues thought my practice habits and through perfecting the game plan and my fundamentals and what I’m being taught and go out there and play for my guys next to me, it’s all going to come together like it has in years past. And this year, it is just not.”

Some on social media are blaming Mr. Kelce’s relationship with Ms. Swift for his struggles on the field. Once considered a good luck charm during the Chiefs run to a Super Bowl victory after the 2023 season, her presence at Sunday’s game, in a suite alongside celebrity friends Selena Gomez, Lena Dunham and Leonardo DiCaprio, didn’t help the Chiefs attain victory.

One fan posted on X, “It’s looking like the Taylor Swift curse is real KC.” Another posted, “Taylor Swift ruined that football team.”

Another took a more humorous route: “Chiefs (are) so bad, Taylor Swift about to call off the marriage to Kelce.”

Despite the long odds, inconsistent performances and celebrity swirl, the Chiefs insist they can steady the ship. But their margin for error is gone, narrowing their season to a simple directive: win every game or the NFL will face a post-season without its biggest box-office draw.