Government Back Stop

As part of the policy proposals regarding residential financing changes, both political parties are pushing the reduced role, if not the complete elimination, of the government in the mortgage sector. The President's proposal is to wind down Fannie Mae and Freddie Mac, but to create a wholly different government insurance program to provide a smaller back stop to securitized mortgage loans. Republican's criticize this approach because they want mortgage lending to be completely privatized. My question is, can the markets ever really be free of a government back stop? If the financial and housing sectors face the kind of meltdown that happened a mere five years ago, can the government take a completely hands off approach and let unadulterated capitalism run its course? It's hard to imagine that it could if businesses and regular citizens stood to lose their actual deposits. If that's the case, shouldn't government have some role in the very system that it will be called upon to "bail out," so as to mitigate, even prevent such a meltdown from occurring in the first place?