He's not, as this excellent Sacramento Bee story makes clear. Brown has had a mixed relationship with labor throughout his political career. His famous frugality as a politician has rankled.
In fact, even as Whitman claims she is facing a "Jerry Brown Inc." collection of unions, real questions remain about whether Brown will get the wholehearted labor support he needs to win. For months, there has been story after story of how the labor calvary was about to ride to Brown's rescue with huge ad buys criticizing Whitman. But the money that has shown up -- and the resulting ads -- have been underwhelming.
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If labor doesn't back Brown big, such a decision might be rational. Brown's independence may make him something less than a good investment for labor. And, with the governor's power limited by a dysfunctional budget system, hvaing an ally in the governor's office is less valuable than it used to be.