On Wednesday Fed chief Ben Bernanke became the first American official in recent memory to admit just how deep a hole we have dug ourselves with our biggest creditor.

Bernanke said China holds at least $2 trillion of U.S. government bonds. That is more than double the widely cited official figure, which is published monthly by Treasury.

As staggering as Bernanke’s number is, his coming clean comes as a relief. As ugly as our debt problem is, it creates problems for China too — what to do with all that paper?

And maybe, just maybe, the more facts that are out there, the better decisions policymakers will eventually make. Emphasis on eventually.

“The monthly Treasury series is wildly inaccurate, but it’s good that someone’s finally willing to say so with the doors open,” said Derek Scissors of the Heritage Foundation. “Perhaps with a reasonable figure available, we can see more clearly the implications of China’s dependence on the dollar.”

Officials in the two countries have been trading jabs lately over each other’s unpopular policies. Both have been easy with money in a bid to spur growth, but Bernanke has taken a beating in China and elsewhere for the recent spike in global food inflation.

For its part, China has spent years holding down the value of its currency to boost exports – a program that is drastically out of favor here with unemployment at 9%.

The dollars it has purchased in pursuing that policy now expose it to big risks: Scissors notes that China stands to lose hundreds of billions of dollars on its Treasury purchases should the yuan appreciate significantly, as U.S. policymakers would like.

Of course, there is also the question of just how the U.S. will pay off on all its promises. Testifying before the House Budget Committee, Bernanke said in response to a question from Rep. Tom McClintock that China holds as much as a quarter of outstanding U.S. government debt – “more than $2 trillion” of Treasury securities.

The comment drew a double-take from McClintock, a California Republican. Apparently referring to the latest official count released by Treasury, McClintock asserted that China’s holdings amounted to around 9.5% of outstanding U.S. government bonds.

McClintock is apparently referring to the latest official count, publicized monthly in Treasury’s major foreign holders table. Those figures, from November, show that China owns $896 billion of Treasurys.

Both McClintock’s and Bernanke’s figures foot fairly well with the $9 trillion of Treasury debt outstanding at the end of the third quarter, according to the Fed’s Flow of Funds report.

But Bernanke’s figure is far more revealing, in that it sheds light on the true size of China’s stake in keeping the U.S. economy rolling. It is in line with the estimate made by China watchers such as Scissors, who says Chinese holdings of Treasury and agency debt – that issued by the mortgage investors Fannie Mae and Freddie Mac – likely range between $2 trillion and $2.5 trillion.

Why do the Chinese hold so many U.S. bonds? It’s not because they like us, sad to say. The huge Treasury hoard is a function of China’s huge trade surplus – Scissors estimates China’s 2010 balance of payments surplus at $471 billion, or $39 billion a month – and the lack of an alternative to the dollar.

“There is no unified European bond market, and Japan is closed to large Chinese purchases,” he writes. “The only market large enough to absorb such huge surpluses is American bonds.”

Scissors has been questioning the official Treasury tally for some time. He has noted, for instance, that China’s official Treasury holdings remained static over the past year – ranging between $846 billion and $929 billion – even as the country ran its massive surplus. How is that possible?

Scissors contends it did so in part by purchasing Treasurys through other countries. Over the past year, Treasury’s tally of Treasurys held in the U.K. – including in the tax havens of the Channel Islands – has surged by $355 billion.

Those sorts of purchases will only continue till China changes its ways — which isn’t going to happen tomorrow, not with a national leadership change set for next year.

“China will not break the yuan’s peg to the dollar until it can resolve the matter of soaring dollar holdings, and that can be done only through financial reform,” Scissors writes.