Depends on who "we" is.
From the perspective of a benevolent dictator that is responsible for maximizing the happiness of all citizens the answer is fairly obvious: no.
If I am someone concerned with the happiness of manufacturing employees and am ok with establishing anti-market, anti-competitive, and extremely inefficient policies, then the answer is less obvious: I don't know, depends on what you can do for me.
A friend recently pointed out the upside of the GM bailout. "...instead of getting rid of tons of their employees when technology revolutionized manufacturing, they actually helped them." The term "they" in this context refers to the architects of TARP, a program initially aimed at financial institutions but was expanded to include GM and perhaps other companies.
A basic economics course hammers home to students the importance of acknowledging that society faces tradeoffs whenever a decision is made concerning economic policy. What was the tradeoff with the GM bailout?
Gains: GM workers benefited. Their pensions, healthcare, salaries, etc were maintained. Also, the country didn't have to worry about selling off GM brands to other companies in order to keep beloved brands alive. You could also argue (though most economists won't) that it's great to keep low-level manufacturing jobs in the United States (it's not).
Losses: First, we want technological advancement in this country, and in the world. Even if it means displacement of workers with low tech skills. Those that lose in this situation can be re-trained, their skills upgraded, etc. The fact that this process may seem difficult should not lead to the conviction that production processes should never be improved through better use of technology, instead it should serve as an indictment of the lack of the U.S. education system's ability to adapt to needs. The loss in this situation is that those low-end manufacturing jobs are SUPPOSED to be lost. Every healthy economy sheds low-end jobs as new technologies emerge the same way that organisms shed deteriorated or damaged cells while replacing them with new and healthy ones. Propping these jobs up only disguises the need for a more flexible work force and education system. Further, it disguises the great disservice unions do when protecting their members from market forces. You can only do it for a little while, eventually someone will have to pay. In the GM bailout case, it is the taxpayer, which leads to the next loss.
TARP and the GM bailout made it clear that middle class taxpayers located in and around Detroit and that belonged to a union were more important to policymakers than those located elsewhere. The bailout amounted to a transfer of wealth from taxpayers in the general U.S. to taxpayers working for the UAW union. Lest you feel sorry for the UAW employees, GM reported that the average wage paid to an employee in 2006 was around $40.00/hr when you include overtime, wage premiums, vacation, and holiday pay. That wage rate, full time, amounts to around $76,000 per year, which is high enough to put one squarely in the upper-middle class.
"But", you say, "it acted as a stimulus!!!" Fine. It stimulated Detroit and kept GM cars in production. This argument is tough to make. First, it assumes that the money that will have to be taken from the taxpayers elsewhere in the country (don't forget, when you spend money, you have to actually collect it at some point) would not have been spent as productively as the government spent it by giving it to a failed automobile manufacturer. Also, it assumes that the public will be better off having not purchased other cars available for consumption such as Hondas, Toyotas, Nissans, Chevys, and Fords etc. This is clearly not the case. The public would probably be better served to, in fact, buy non-GM vehicles. You may disagree, but at the minimum, it's a wash. And if one argues that it is better to buy American than foreign vehicles, then I'll save the haranguing you deserve for another post.
Lastly, why would the government want to establish the following precedent: private companies that demonstrate an inability to generate profits will be purchased by the government and have their non-profitable good or service subsidized by the American taxpayer? They shouldn't want to. Unless, their motives are incompatible with the principles of free-enterprise.