I'm not entirely convinced there's a net benefit. Paying GM 25B to continue to use materials and labour inefficiently, creating vehicles that won't sell, provides a reason to give their workers a salary which they'll spend in their local economy, keeping second-order collapses like those that accompany the closing of military bases in isolated areas from happening.
If, on the other hand, we shut down GM and put its former workers on extended unemployment, those with the aptitude and will relocate and find similar jobs; those without retrain and join the economy in a different role. The materials that formerly went into unwanted cars will be obtainable more cheaply for other uses.
The point is debatable, but it seems obvious to me that even if some of the GM workers remain forever unable or unwilling to rejoin the workforce, the cost of supporting them will be lower without the inefficiency of supporting a company on top of them.
I've read, but cannot source at the moment, that when federal aid to farms really took off in the 1930s, they did the math and realized welfare to individuals would be cheaper. For a variety of reasons, they implemented price controls instead, and saddled the economy with a persistent market failure in food production that's now over 70 years old.
It's not like the government isn't planning to extend unemployment benefits because of the economy.
If GM goes bust now then more people will be on the dole for longer.
The tax payer pays for it one way or another.