Do we build them up or knock them down?

Step one: avoid a run on the bank. Check. Step two: recapitalise. Er, we'll get back to you. Step three: stop this from ever happening again. Um ...

When Hank Paulson bounded down the steps of the US Treasury a week ago to promise the US government would do whatever it takes to prop up Fannie Mae and Freddie Mac, he raised more questions than anyone was able to answer.

This weekend the Treasury Secretary is still fighting to persuade a sceptical Congress that it should write him a blank cheque to lend money and buy shares in Fannie and Freddie. Republicans, in particular, worry that the taxpayer could end up on the hook for tens of billions of dollars.

With more and more US homeowners defaulting and house prices collapsing in many parts of the country, reducing the value of Fannie and Freddie's collateral, no one knows how much money the companies might end up needing.

But while the politicians grapple with these issues, others are just starting to examine how the crisis might reshape the US mortgage market and Fannie and Freddie's place in it. Specifically, now Mr Paulson has made explicit what was previously only an implicit Treasury guarantee of Fannie and Freddie debt, can we go back to the status quo ante? Has everything changed, or nothing?

Other questions: can the pair keep doing the government's business of providing Americans with access to cheap mortgages and a slice of the American dream, while operating as companies quoted on the stock market, tapping investors for capital and rewarding them with dividends?

They have shown they pose a danger to the financial system as they stand. Does that mean they should be shrunk in size? Would giving Wall Street's banks incentives to compete create a vibrant and stable enough secondary market for mortgages, allowing the ultimate privatisation of Fannie and Freddie?

Or, in the other direction, does their pivotal importance to housing mean they should be nationalised completely, putting the full heft of the Treasury's balance sheet behind them and allowing them to fulfil Fannie's depression-era remit – stimulating the mortgage market during the periodic credit crises when Wall Street fails to do so?

These questions depend on what happens in the coming weeks and months, and then on the political hue of Congress and the White House after November, says Bill Maloni, Fannie Mae's former lobbying chief. "It is important to note that neither company has asked for federal help," he explains. "The situation is filled with lots of hype. I don't think either is as badly off as many suggest.

"But if the federal 'help' becomes reality then ... changes of personnel, limits on their portfolio growth and the unwinding of existing portfolios would probably be some results."

A Barack Obama administration and a Congress controlled by Democrats, who are traditionally more favourable to Fannie and Freddie, could undo any moves to shrink the two companies, says Mr Maloni, and even the Bush administration has been considering a "conservatorship" that would take ownership of the firms if all else failed.

But some Republicans, notably the presidential candidate Ron Paul, lay much of the blame for the credit crisis at Fannie and Freddie's door and say the market would be more efficient if they did not exist.

Kevin Logan, senior economist at Dresdner Kleinwort, says: "They have contributed to cheaper mortgages and more homes being built than would be economically rational in a private system, so in that sense they are channelling capital in an inefficient way. The mortgage market could live without it, the housing market could live without it, but it is a question of getting from here to there. "

A free market solution might only exacerbate the credit market convulsion, where "non-conforming" loans have become almost impossible to come by. That was the situation in the depression that led to the creation of Fannie Mae.

Some economists have begun arguing for regulators to rethink the amount of capital they demand that financial institutions should hold, saying at least some rules should be counter-cyclical so not everyone has to pull out of the credit markets at the same time.

It is not just the US housing market that is difficult to imagine without Fannie and Freddie. The global financial system relies on their debt and the mortgage-backed securities they fashion from millions of individual home loans. Some $1.54 trillion is held by overseas investors, up ninefold from a decade ago.

Greater regulatory oversight of Fannie and Freddie is a given, but it is hard to see a path to a radically different structure for the US government's involvement in the mortgage market. We learnt last week they are too big to fail. We might also find they are too big to change.