Romney and Obama essentially supported the same plan, a unique structured bankruptcy, although the details were different as Obama did more to protect union interests. The “bailout” Romney objected to was a no strings handout that the car makers originally asked for. You just have to read what he said:

Romney: Let Detroit Go Bankrupt

More here at TPM:

Then a funny thing happened. The new Obama administration came in and, rather than continuing to write a “bailout check,” did just what Romney had recommended. GM and Chrysler were forced to go through a managed bankruptcy in which the government provided the loans and guarantees needed to keep them afloat. In exchange, workers and bondholders had to make concessions.