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To answer your question: Yes, Matt Cassel will be starting for the KC Chiefs next week.
Romeo Crennel opened up his postgame press conference following Sunday's game against the San Diego Chargers with a few remarks to the media and without being questioned he said Cassel would remain the Chiefs starting quarterback.
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"I know there will be some questions about the quarterback. I'm staying with the quarterback and I stayed with him during the course of the game. I stayed with [Jamaal] Charles during the course of the game. And we're going to stay with him going forward at the moment."
I should highlight: "...at the moment." In reality, every position is "at the moment" because any coach would make any switch necessary to get a win.
But I think the Chiefs coaches are realistic -- Brady Quinn isn't obviously better than Cassel. There's the argument there for change for change's sake if things keep getting worse and maybe I can understand that.
Danny Parkins of 610 Sports asked Cassel during his postgame presser if Romeo had talked to him about making a change, and Cassel said no.
The turnovers have to stop. That's problem No. 1.