A few points:
1. As mentioned before, there is precedent with Chrysler in 1979. The constitutional authority for this is the Commerce Clause, and at least this is obviously related to interstate commerce. The case Wickard v. Filburn in the 1940's greatly expanded the interpretation of this clause, when it was held that a farmer growing wheat on his own land for his own consumption could be regulated under this clause. Since then, I believe there were only two cases the federal government lost in arguing that they were empowered to regulate under the Commerce Clause.
Like it or not, this is how the courts have ruled.
(As an aside, this is also the clause under which national health care advocates argue that the federal government is empowered to act).
2. The Chrysler bailout didn't cost US taxpayers a dime. Arguably, it saved them money, through the taxes paid by the Chrysler employees.
3. For those who argue for a laissez-faire policy of "let them fail", the present system is hardly laissez-faire. There are many, many government regulations on the industry, and they add cost to the vehicle. While all manufacturers face the same regulations, so the playing field is level, as the cost of cars go up, the number of people who buy them goes down. People drive their cars longer, and so buy fewer of them, so GM sells fewer of them.
Additionally, the Sherman Anti-Trust act has the unintended consequence of placing US manufacturers at a relative disadvantage. As Lee Iacocca put it, "GM and Toyota can form a joint venture to put Ford out of business, but GM and Ford can't form a joint venture to put Toyota out of business."