Kansas City, Mo. ? Unfortunately for Kansas City, Larry Johnson’s record-breaking rushing day against the sorriest team in the NFL counts for only one victory.

Now begins the toughest part of the schedule for the playoff-hopeful Chiefs (6-4). Their last six regular-season games are against winning teams.

Five of their upcoming opponents either are outright or co-leaders of their division, and the sixth, San Diego, already has beaten Kansas City once.

Denver (8-2), New England (6-4), Cincinnati (7-3) and the Chargers (6-4) will be at Arrowhead Stadium, starting Sunday with the defending Super Bowl champion Patriots. Sandwiched between the home games is a two-week span in mid-December when Kansas City visits NFC East leaders Dallas (7-3) and the New York Giants (7-3).

Gone are soft touches such as the Houston Texans, who gave up a Johnson’s franchise-record 211 yards rushing Sunday night in Kansas City’s 45-17 victory.

It may not be the toughest finishing stretch of games in Dick Vermeil’s coaching career, but it’s close.

“I don’t know if it’s been six games, but I know there have been times when we’ve had to finish strong,” Vermeil said Monday.

Fortunately for the Chiefs, their painful and expensive rebuilding effort seems to be paying off on defense. Buffalo and the Texans in the past two weeks have been held down.

“I’ve seen improvement all along,” Vermeil said. “You play a team like (Houston) and it’s a little more glaring because they haven’t been a productive offensive team.”

So, can the Chiefs’ ascending defense meet the challenges of the next six weeks?

“I believe we can. Time will tell,” Vermeil said.

One of the main newcomers in the defensive improvement, however, was on crutches after the Houston game. The Chiefs said cornerback Patrick Surtain had a right ankle sprain, not a good sign considering the next six opponents all rank in the top 12 offenses in the league.

Also injured was long snapper Kendall Gammon and reserve linebacker Kris Griffin. Gammon had what was described as a bruise on the lower left leg and Griffin a hamstring injury. The long-snapping duties were passed to defensive end Jared Allen, who learned the skill in college at Idaho State.

“I don’t know where (Surtain) will be,” said Vermeil. “Same for Kendall Gammon, Kris Griffin.”

The good news on the injury front centered on the injured hamstring of Pro Bowl left tackle Willie Roaf, who has missed several games.

“He will practice full speed on Wednesday,” Vermeil said.

Vermeil was in no mood to take Johnson to task for refusing to speak with reporters Sunday night after his record-breaking day. After Chiefs officials tried to set up a news conference, they returned to say Johnson was not talking.

The third-year running back, who has rushed for more than 300 yards in two games since Priest Holmes went on injured reserve, has felt he was not always treated fairly by the media.

“A certain percentage of the media has enjoyed writing any time he’s been in trouble. I think it was his way of just saying, ‘to hell with you,”‘ Vermeil said. “He does have that right. His name has been in the paper a lot, and it’s more about problem things.”