From what I've seen, Fannie/Freddie must be propped up in some way, even though they are ticking bombs, reportedly with 80-1 leverage. Adding their $5 trillion in debt would effectively double the current national debt (over $9 trillion, of which about $4 trillion is owed to social security, leaving $5 trillion owed to others). That doubling would cause far more and far larger problems than it cured. So the GSEs must stay alive for now, hopefully to be quietly wound down and dismantled when the time is right.
Freddie and Fannie's debt is backed up with collateral -- houses, to be exact. Most mortgage holders who own these houses are making their mortgage payments on time.
If Freddie and Fannie went into conservatorship, the US would be responsible only for the delinquencies -- Fannie and Freddie guarantee the interest rate return to holders of their mbs. The Barrons article suggested that could be $100 billion.
That means most of the debt the government would assume gets paid back by the mortgage holders, not the taxpayers.
And the cost would be less under public ownership, because freddie and fannie would no longer be paying dividends to shareholders -- that dividend money would stay in the US Treasury.
That amount of money is manageable. Not only that, it would settle the market, bring down mortgage rates, goose the economy, and probably help stem the decline of the dollar.