Yes, both Obama and Romney favored the companies going through managed bankruptcy. But the US auto industry entered its own existential crisis as the world economy, particularly credit markets, were at a standstill. Even with government guarantees there was no private capital for the GM and Chrysler to power to keep them functioning as they went through the bankruptcy process. And that was the rub. Government guarantees weren't enough. The government had to write checks and at a moment when bailouts of all sorts had become politically toxic.
Romney said no. Obama said yes. Without those funds -- politically unpopular and with little guarantee of a return -- the car companies would go into liquidation bringing down not only themselves but lots of associated companies and suppliers with them. We know this is what he said at the time on multiple occasions but now Sam Stein has dug up yet another interview from the time in which Romney claimed that direct government money would be the end of the US auto industry.
For where Romney stood at that moment, saying no to any more bailouts was the politically expedient thing to do and it looked like a good long term political bet. The details of just what happened and the fact that Romney really would have let Detroit 'go bankrupt' in the liquidation sense of word has been distorted and obscured no end. But in the final analysis people in the bit auto industry states seem to get it.