Some critics warn that the suggested replacements gloss over the private sector's role in producing lots of shoddy mortgages. 'All of the proposals we're seeing have one thing in common: They would essentially give greater control over the market to the biggest banks that were key participants in the bubble,' said Joshua Rosner, managing director of research firm Graham Fisher & Co. and a longtime critic of Fannie and Freddie before their collapse.

Fannie Mae Chief Executive Timothy Mayopoulos is prodding Washington to make up its mind. He says he is concerned that continued calls for liquidating the company could send his best employees for the exits. They 'have families to feed,' he said in a May speech to officials from the nation's biggest banks.

After Fannie reported a $58.7 billion profit during the first quarter, in part from reversing certain write-downs it had taken after the bust, it launched the online 'progress report' that touts its recent achievements, including charitable giving.

Compared to Freddie Mac, 'the culture at Fannie has always been much more self-confident, much more 'We're going to survive this thing,'' says Robert Bostrom, former general counsel at Freddie Mac.

Mr. Mayopoulos didn't endorse a particular outcome in his May speech. But he reminded the bankers that 30-year, fixed-rate mortgages weren't a 'naturally occurring phenomenon in financial markets.' And there was 'limited evidence,' he said, that private capital was ready to return in large scale.

'We fully appreciate that Fannie Mae should play a smaller role in a properly functioning market,' he added, 'and we are working to make that happen.'