Detroit auto executives advocate "government getting a stake in the auto companies that would allow taxpayers to share in future gains if they recover" ...
I remind these executives that each American is already perfectly free and able, with no action from government, to "get a stake" in these companies. Of course, few Americans now choose to do so - a fact that reflects the considered judgment of millions of people that these companies are unworthy recipients of investment funds.
This is an example where pure libertarianism gets you quickly to the right answer. Lose the "we," and instead ask, would I undertake this policy myself? That is, would I lend money to the auto makers? If the answer is that I wouldn't, then the implication is that "we" shouldn't.
The same reasoning applies to giving money to financial firms. I wouldn't, therefore we shouldn't.
Picture everyone in Congress who voted for TARP standing on a street corner in a Santa suit, ringing a bell, and asking for donations to pay for the rescues of AIG, Citigroup, and so forth. In a libertarian society, that is what they would have to do in order to fund the bailouts.
If that image doesn't move you in a libertarian direction, then nothing will.