Saints to interview Mike McCarthy at the end of this week near Jan 29-Feb 1 [Underhill: McCarthy would have to be the current favorite]

webster said

Our next coach will stick with Carr or another proven qb, they won’t risk their career on a young unproven player. I could see a new coach bringing in some young qbs to develop for the future.

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Next coach is getting 3-4 years minimum. Chances are, if you bring in a McCarthy, he's gonna have a lot of say with the roster and draft+future FA signings. If you hire one of those other guys who are 1st time head coaches, maybe not so much. Payton only got that kinda cachet because he got to the NFC title game in year 1.