I see your point and agree but if you were running a US car company how would you go about completing with the Asian cars being dumped in the US where the daily wage is less than a hour of UAW wages.
I'm not exactly sure where you think a lot of the Asian cars are "dumped" into the US on sweat-shop labor. I've got friends who work for Honda who make a pretty penny, as do the folks down the road from me here in Alabama at the Hyundai plant. Where exactly do you get this sort of wage data from? I've talked with people online (through forums and such) who work at Toyota plants in a couple of different spots across the country, and they are all well-paid. And I wouldn't believe that the auto workers in any civilized country (i.e. Japan) get paid peanuts for what they do.
My point being that the only investment into the US auto industry seems to be from foreign companies. While GM is investing in Mexico and laying off American workers, other foreign companies are building plants here and investing dollars into the auto industry.
I'm a staunch believer in the fact that UAW brought (and continues to bring) a lot of hardship on themselves. I don't like unions and I think their purpose has long since passed. I work at a place with unionized labor (for the hourly folks).... and well..... yeah.....
But to answer directly as to how the American companies could compete with lower costs labor of the foreign (yes, I know that the foreign manufacturers do pay less than those who employ UAW workers, although I highly doubt it's at the day's wage/UAW hour fraction you posted above) GM could always put a deal on the table and tell the union that's that. If it costs so much in labor to build a vehicle that the consumer price wouldn't allow it to sell, what would the union workers do then? I know it's not that simple, yet I also know that no worker is ever irreplaceable. Union workers can be replaced. GM could also streamline their product offering - There's no reason to have exact-brother models of GMC and Chevy pickups, vans, SUV's, etc. And they could also quit hanging their future hopes on novelty ideas like the Volt. {Just a couple quick examples, since you asked what *I* would do.}
I know of two serious attempts at the Honda facility to unionize here, and I believe it's been shot down by employee vote both times. That says a lot about what folks here who make a decent wage and are treated pretty nicely by Honda think of the union. I think it also says a lot about how well the Honda group treats the employees here. I don't see anyone working for the foreign automakers that makes $20 per day - I think it's a little naive to believe a figure like that.
To me, it's a slap in the face for GM to go invest our bailout money in a Mexican operation. I think it's asinine and I think it shows that they're still going to make poor decisions because they believe we won't let them fail. At some point, you gotta cut the cord and let them learn to swim or let them sink.