The hole at the corner of 15th and L streets, in downtown Washington, is deep -- and getting deeper.

Earth-movers there are laying the foundations of a shiny new headquarters for Fannie Mae, the bailed-out giant of American mortgages.

But the sleek design, replete with glass sky bridges, belies a sober reality: Fannie Mae and its cousin, Freddie Mac, are once again headed for trouble.

In fact, there’s almost no way around it. On Jan. 1, 2018, the two government-sponsored enterprises will officially run out of capital under the current terms of their bailout. After that, any losses would be shouldered by taxpayers.

Granted, few people are predicting a disaster like the one in 2008, when the GSEs had to be thrown a $187.5 billion federal lifeline. But eight years later, people still don’t agree on what to do with these wards of the state. In Washington and on Wall Street, the fight over Fannie and Freddie drags on.

“Everyone agreed that this was a broken business model that made no sense,’’ said Douglas Holtz-Eakin, president of the American Action Forum, a center-right advocacy group in Washington. “Now, inertia is driving the way.’’

The stakes are high. Earlier this month, the Federal Housing Finance Agency, which oversees the GSEs, said Fannie and Freddie might need a $126 billion rescue if the economy were to stumble hard again. In recent years the Treasury has collected more than enough money from the GSEs, in the form of dividends, to cover a bill of that size.

But to the GSEs’ critics, the real issue is that policy makers have yet to come up with a long-term plan. Republicans want to kill the quasi-governmental companies. Democrats have floated the idea of merging them. Hedge fund managers like Richard Perry have gone to court to claw back dividends swept up by the Treasury.

And so one of the thorniest financial questions of the early 2000s -- what role, if any, should the federal government play in America’s $10 trillion mortgage market -- will now fall to the next president. So far, neither Hillary Clinton nor Donald Trump have seized on the issue.

The good news is that taxpayers have recouped their bailout money, and then some. By September Fannie Mae and Freddie Mac will have routed to the U.S. Treasury some $251 billion in dividends on senior preferred stock that the government acquired in the rescue. The GSEs have paid those billions to the Treasury, rather retain any of the money as operating capital.

FHFA officials say this controversial arrangement -- instituted in 2012, the very year the GSEs returned to profitability -- make another rescue, however small, all but inevitable. The regulator has quietly examined whether it can suspend the payments unilaterally to build up the GSEs’ capital cushion, among other options.

‘Serious Risk’

“The most serious risk, and the one that has the most potential for escalating in the future, is the enterprises’ lack of capital,” Mel Watt, director of the FHFA, said in a speech in February.

Also at stake are Fannie and Freddie preferred shares, with a face value of $33 billion, along with common shares, potentially worth even more.

Investors including Perry and Bill Ackman, another prominent hedge fund manager, have sued over the bailout terms, so far with little success. A federal judge dismissed one suit in 2014; an appeals court is expected to decide soon whether the investors deserve damages or at least another shot at making their case.

“We only need to win one of those claims in any of the courts in order to ultimately be successful on the legal front,’’ Ryan Israel, a partner at Ackman’s firm, Pershing Square Capital Management, said on a conference call with investors in July.

Stark Differences

The differences are equally stark in Washington. The 2016 Republican party platform has characterized Fannie Mae and Freddie Mac as a “corrupt business model” that has enabled executives and investors to reap the profits while sticking taxpayers with the losses.

In the Democratic camp, two Clinton advisers, Gene Sperling and Jim Parrott, have said they favor merging the GSEs into a single government-owned corporation. In a March report, the two men, former advisers with the National Economic Council, and other authors suggested that the new organization be required to sell mortgage credit risk to private investors, thereby taking taxpayers off the hook for most future losses.

‘Original Problem’

“I’m concerned that we exit this situation without fixing the original problem,’’ said Representative Ed Royce, a California Republican who sponsored a bill last year that quashed pay hikes for the companies’ chief executives. “The status quo of a nationalized mortgage market is unsustainable for taxpayers.’’

None of this was supposed to go on for so long. When Fannie and Freddie were placed into a conservatorship under FHFA, most policy makers viewed the move as a short-term fix until Congress came up with a full solution.

Politically, the idea of preserving them was considered “patently absurd,’’ said Parrott, who helped lead housing-finance reform efforts for the White House from 2010 to 2013. “Eliminating Fannie and Freddie was a prerequisite for discussion.’’

Plenty of ideas have been floated. Former FHFA Director Edward DeMarco and ex-Senate Republican staffer Michael Bright have proposed turning the GSEs into lender-owned insurers. Others have suggested transforming them into what amount to mortgage utilities, with capped rates of return, essentially keeping them in place in a more regulated form.

Royce says he and other House Republicans plan to introduce a bill as early as September that would require Fannie and Freddie to transfer more risk to the private market and give private institutions access to a technology platform for securitizing loans.

John Taylor, who leads the National Community Reinvestment Coalition, says GSE reform proposals will fail. Think-tank libraries “are filled with all these treatises with proposals from a year to 40 years ago that are simply gathering dust,’’ he said. In all likelihood, the latest proposals “are going to end up in the proverbial stockpile.’’