There are lots of rumors about Brizard's job being on the chopping block, and I have no reason to assume there's not some truth in them. (John Kass calls Brizard Emanuel's "human shield.") There's no shortage of folks who would welcome the possibility of his departure, including angry teachers and frustrated insiders and anyone who doesn't like the Mayor. But here's the thing: there's no good argument for letting Brizard go (beyond Mayoral convenience), and there are many for having him stay on. So be careful what you wish for.
With some relatively minor exceptions, Brizard isn't to blame for most of what's gone wrong at CPS in the last year -- that's on Emanuel. The premature declaration of the longer year? Emanuel. The embarrassing "Pioneers" program? Emanuel. The senior staff that was hired along with Brizard? Emanuel. The antagonistic relationship with the teachers? Emanuel. Brizard might not have shown himself to be a brilliant leader but the main mistakes of 2011-2012 weren't his.
Brizard's departure wouldn't change much - in fact it might make things quite a bit worse. Changing agency heads in short order, during the middle of a school year, is a recipe for inertia, if not disaster. Firing Brizard would in some eyes take Emanuel off the hook, which I don't think does anyone any good. There's no obvious candidate to replace him who would do any better.