Fannie Mae didn't start out as a "GSE," it started out as a government agency. It can go back to being a government agency if the government needs to further the economic goals of liquidity in the home mortgage market--and maybe it can go back to doing business with Podunk National, rather than lavishing its capital on mega-lenders who aren't going to be subject to regional liquidity crunches. All this uproar over "nationalizing" the GSEs seems to me the part that is really overblown. If they can't raise enough capital as shareholder-owned entities to prevent the necessity of periodic bailouts, then let's end the experiment with "GSEs" and make them agencies of the government. Any "rescue" that doesn't wipe out the shareholders is simply making a bad thing worse.
Brad Delong says this is the "Laura d'Andrea Tyson line on the GSEs" as well which reminds me that I've been meaning to wonder aloud if she's going to be our next Secretary of the Treasury.
At any rate, I'm only a lowly blogger but the idea of "government sponsored entities" doesn't make a great deal of sense to me. The things we need government agencies to do should be done by government agencies, other things should be done by market actors who are subject to ordinary risks.