Last time I read up on this, I was led to believe that the regulations were only a minor factor, and the main thing driving the subprime explosion was demand in the investment market for misleadingly-rated mortgage-backed securities.

My understanding of the details is almost nonexistent, but I gather that there was some kind of statistical wizardry that let lenders load up a bunch of crappy mortgages into a package that was, in aggregate, supposedly an extremely safe investment with a very attractive return. These securities became the primary product, with the mortgages themselves being the raw material. The market demanded that production increase, so the lenders did the finance equivalent of drilling for tar sands oil. At this point there was no need for the government to mandate subprime mortgages. Lenders weren't just grudgingly implementing policy, they were enthusiastic, shouting from the rooftops for people to apply for mortgages even if they thought they wouldn't qualify. I clearly remember Countrywide's motto: "No one can do what Countrywide can". I guess it turned out that Countrywide couldn't do it either.