"The Bailout Paradox" Paradox

Robert Reich, the nation's 22nd Secretary of Labor and a professor at the University of California at Berkeley, presents an interesting take on the Big 3's problems, deeming it "The Bailout Paradox". Specifically, he states:

As a condition of getting a federal bailout, the Big Three are promising, among other things, to cut costs. Among the costs to be cut will be jobs. This is paradoxical, since the reason Congress is considering bailing them out in the first place is to preserve jobs and avoid the social costs of large-scale job loss unnemployment insurance, lost tax revenues, pension payments that have to be picked up by the Pension Benefit Guarantee Corporation, and so forth).

We should take a lesson from the Chrysler bailout of the early 1980s. The ostensible reason Congress voted for it was to preserve Chrysler jobs. Yet once the bailout was underway, in order to generate the money it needed to restructure itself, Chrysler laid off more than a third of its workforce. Most of these jobs never came back.

The paradox of this argument stems from the UAW absurd labor benefits and costs to the automotive companies. Isn't cutting costs (jobs) in order to prevent bankruptcy or total failure (total loss of all jobs) the idea? I'm against an automotive bailout for demand issues, but no matter how you slice it, Detroit needs to reduce its costs related to labor.