I think you answered your own question. Who says GM won't eventually fail, they are still a frail corp. even after the infusion of nearly $100 billion? It would appear the midwest isn't much better off in spite of the WH action.
Nothing says they won't still fail. But with Obama's actions, they have a chance, and at the very least, there may yet be a buyer now, with the economy improving.
Bottom line was at the time, they had two choices: bail them out and take a chance at saving all of those jobs, or let the company fail, and see where the chips may fall.
Given that the rest of the economy was so uncertain and many doubted that the country could take the additional strain, I think they made the right choice.
And by the way, don't forget that the jobs at risk did not just apply to GM in particular, but to all the industries that provided GM with materials - including the steel industry, plastics, electronic components, etc.
It would have meant 100s of thousands of additional jobs losses - possibly millions - and all concentrated in one part of the country. It would have been devastating for those states to deal with >20% unemployment rates, loss of revenues, budget balancing, etc. The ripple effect would have potentially hurt everyone.