The Joint Chiefs of Staff, says its chairman, Adm. Mike Mullen, has a “physics problem.”

According to a 2008 accord between the United States and Iraq, the US military is to be evacuated from Mesopotamia -- down to the last tank mechanic and dishwasher -- by the close of the calendar year. Lately, there have been hints that Iraq might want a “residual force” of as many as 12,000 troops to stay, but nothing firm.

Hence Mullen’s dilemma: How does the Pentagon plan for withdrawing its personnel and equipment when it doesn’t know for sure how many soldiers will be leaving? There are only so many C-130s to load and so much time in which to load them.

In Iraq, this question is a burning political issue, one that could threaten the government of Prime Minister Nouri al-Maliki.

Maliki has invested major political capital promising to end the US occupation in accordance with the 2008 pact, telling the Wall Street Journal in December: “This agreement is not subject to extension, not subject to alteration. It is sealed.” His ruling coalition is fragile, and key partners intend to hold him to that promise.

But there’s precious little debate in Washington on the date for withdrawal. Even though President Barack Obama campaigned on a pledge to leave Iraq, his administration isn’t telling Maliki that the troops are decamping come what may.

To the contrary, the White House puts out regular signals that thousands of soldiers will stay if Iraq “requests” it. The feelers are so frequent that Obama seems to be asking Iraq to request that Washington extend its military sojourn.

In fact, there’s growing bipartisan consensus that a prolonged “residual” occupation of Iraq is a good thing. Republican presidential candidates, eager to attack Obama on Afghanistan and Libya, say next to nothing about Iraq. The unreconstructed neoconservatives quietly advising most of them proclaim in public that departure from Iraq is premature. Most Democrats are content to silently follow the White House.

The Obama administration and the Maliki government, each for its own reasons, are both hedging the bet they made when they signed the withdrawal timetable. Washington wagered that Maliki would widen his coalition to embrace enough political opponents that his government would be stable without an American prop. The Iraqi premier gambled that, with US funding and training, his security forces would grow strong enough to defeat his domestic foes by the end of 2011.

Both bets were foolish, but Washington’s was more so. Maliki and his circle have no serious record of conciliatory politics, and indeed have played upon and exacerbated the country’s sectarian, ethnic and ideological divides to remain in office. In such partisan maneuvers, they have felt secure in the knowledge that tens of thousands of heavily armed Americans are their formidable first line of defense. Theirs is a high-risk game, however, and they are giving every indication that they still want their praetorian guard.

Ultimately, Obama’s vow notwithstanding, neither Democrats nor Republicans are likely to say no if Iraqi politicians wish to cling to thousands of American protectors or so for years to come. The reason isn’t physics, but geology -- the voluminous pools of oil lying underground in Iraq and neighboring countries. American politicians as diverse as Jimmy Carter and Dick Cheney have long believed that the United States must project force in the petroleum-rich Persian Gulf for the sake of the world economy and Washington’s superpower status. The costs have been secondary in their calculations, and the mainstream media does not probe too deeply in areas where both major parties concur.

In Iraq, this ill-advised consensus has thus far cost Americans some $780 billion, taken nearly 4,500 American lives, and severely wounded an additional 22,000 men and women -- to say nothing of the greatly higher tallies of killed and maimed Iraqis. In 2011 and 2012, it will be up to ordinary Americans to compel, at long last, an honest national conversation about Iraq.