What will the winner of the Nov. 6 presidential election do about heading off sequestration — the across-the-board reduction of $1.2 trillion in government outlays over the next 10 years? Included is $500 billion that must come from future defense spending.

In the eight weeks after the polls close, a lame-duck Congress, which has been incapable of dealing with the problem for 11 months, must pass legislation that reduces the deficit by the required $1.2 trillion or the cuts in defense and non-defense spending begin to take place Jan. 3, unless Congress takes some other legislative action and the president approves it.

That formidable task will be aided or complicated by the fact that the Bush tax cuts for middle- and upper-income households are also set to end Dec. 31.

The fog of war is probably clearer than the mystery of what President Obama or Mitt Romney would do before this year ends to head off the cuts required by the 2011 Budget Control Act.

One key player will be Obama, no matter the election outcome. Romney will be another, but only if he is president-elect. Republican and Democratic leaders in the House and Senate have so far maintained their basic uncompromising positions, though bipartisan groups of legislators have tried to find some common solutions.

Both candidates have said that they want to prevent sequestration, but neither has said how he would do so.

At Monday’s debate, Obama said flatly, “It will not happen,” without offering specifics.

Obama will have the upper hand if he’s reelected. He can use the end of the Bush tax cuts as leverage to force a deal with Republicans. That probably would see his desired return to the Clinton-era rates for incomes above $250,000, while making permanent the current rates for those earning less. Additional revenue could come from increasing rates for estate, dividend and capital gains taxes and closing tax loopholes while reducing some corporate rates.

Obama has said he could accept some cuts in domestic programs, and possibly a minimal amount in defense while agreeing to work out savings through Medicare reforms.

The problem will be more difficult should Romney win. Republicans, particularly in the House, have indicated that they want to put off any sequestration action for a year, at a minimum on the defense side, to give a Romney White House a chance to come up with a new plan for taxes and spending.

Obama, however, has said he would veto any such legislation. He also will have the power to let the Bush tax cuts lapse should he decide to veto any attempt by Congress to extend those tax cuts for the wealthy.

Romney has been silent on what he would do. But his speeches and policy statements promise sharply increased defense spending, a 20 percent reduction in personal income taxes at all levels, along with maintaining — if not reducing — rates on dividend and capital gains taxes for the middle class. He has claimed that capping tax deductions for the wealthy and closing loopholes along with reducing non-defense discretionary spending by 5 percent will solve the problem. Most budget analysts disagree.

Still, none of those steps proposed by Romney are likely to occur during the lame-duck session, leaving any solution to sequestration still pending.

Meanwhile, in the campaign, Republicans are calling sequestration an Obama plan to “cut $1 trillion” from defense spending. In a TV spot released Tuesday by the Romney camp, the candidate says: “I will not cut our military budget by a trillion dollars, which is a combination of the budget cuts the president has. That’s unacceptable to me.”

Romney is combining the $500 billion from sequestration with the $487 billion reduction over 10 years that was agreed to by the GOP and Democrats in the Budget Control Act. The first $50 billion portion is contained in the fiscal 2013 defense budget legislation already approved by the Republican-controlled House.

On Tuesday, the day after the debate, Obama again avoided discussing the lame-duck session. Instead, he told the publisher and editor of the Des Moines Register in a phone conversation that in the “short term” sequestration would be a forcing mechanism when combined with the Bush tax cuts to solve the problem. But the president said it would take six months to get done and “will probably be messy. It won’t be pleasant.”

Obama said he was “absolutely confident that we can get what is the equivalent of the grand bargain that essentially I’ve been offering to the Republicans for a very long time.” That offer has been $2.50 worth of cuts for every dollar in increased revenue. He also has proposed working to reduce the costs of our health-care programs.

At the Pentagon, however, planning for sequestration is underway. At a news conference Monday at the Association of the U.S. Army convention, Army Secretary John McHugh said, “We can’t make absolute determinations because, you know, there are still a lot of things at play here.”

McHugh, who spent 17 years as a Republican congressman, said he’s optimistic that after the election there will be a settlement before sequestration can hit. Capitol Hill leaders, he said, “understand the consequences of this better than most and will do everything they can to avoid it.”

Let’s hope he is right.