Explain to me

I'm having trouble with the failure of the automotive bail-out bill. As I've posted before, I've been kind of agnostic on the merits of the bail-out per se, but the reasons it failed in the Senate confound me.

What I don't understand is this: the GOP is ostensibly the party of tax cuts, correct? The argument, as I understand it, is that the government should let Americans keep as much of their money as possible, believing that they know better how to spend it than the government does. Am I right so far? So how can the same party seek to have American workers make less in the first place? I know the GOP hates unions almost as much as they hate taxes, but are they really going to argue that steep cuts in worker pay are a deal-or-no-deal requirement? Are they not essentially saying that they're willing to give the automakers government money so long as less of it goes to unionized workers?

Am I wrong in thinking this is rife with cognitive dissonance?

Update: There's a discussion about these issues, which I will admit I don't totally understand, over at The Plank. I will agree with the comments there that the economy can't sustain the loss of the auto industry because there is no "solvent" entity that can either buy the current Big Three assets as they are, or can restart the auto industry in the foreseeable future.

Update #2: More discussion over at Politico's Arena.

Update #3: For a contrary take from a woman who is orders of magnitude smarter than me about economics, I give you Megan McArdle.