It’s widely assumed that Democrats will have to give up their insistence on a tax increase if they want a budget deal to replace the automatic spending cuts known as “the sequester.” Politico’s Manu Raju and Carrie Budoff Brown reported on Oct. 27 that President Obama had already signaled that he’s willing to negotiate a deal without a tax increase. Thus when Jason Furman, chairman of the council of economic advisers, met with reporters on the morning of Nov. 4, the Wall Street Journal led not with what Furman said but what he didn’t say. He didn’t say flat-out that no deal would go forward without a tax increase.

Far more interesting was what Furman did say, in passing, about the sequester. He said that in the next round of sequester cuts, scheduled to take in effect in January 2014, all of the cuts would come out of defense spending. That happens to be correct, and this simple, little-discussed fact puts a pair of aces into the Democrats’ hand. Unfortunately, it isn’t clear that President Obama (whose poker-playing skills aren’t always top-notch) has noticed.

The Obama-will-have-to-give-up-his-tax-increase story plays into the prevailing press narrative that the Republicans possess all the leverage in the budget talks—even though they just got their clocks cleaned when they tried to block implementation of Obamacare, first by shutting down the government and then by threatening not to raise the debt ceiling. In the current budget talks, according to this interpretation, Republicans wield a much bigger stick: the sequester.

No one dreamed congressional Republicans would tolerate the 2013 sequester, because it slashed defense spending along with non-defense discretionary spending (while exempting automatic-spending programs like Medicare and Social Security). Republicans hate to slash defense spending! But the House GOP surprised everybody by tolerating the sequester just fine; this new breed of Tea Party reactionaries, it turned out, didn’t care nearly as much about defense spending as its predecessors had.

Even so, the next round of sequestration cuts will put that blasé pose to a very severe test. Under the 2014 sequester, defense spending will drop about $20 billion (off a base of about $518 billion), or roughly 4%. Non-defense discretionary spending, meanwhile will remain flat, at about $469 billion. Indeed, technically it will go up slightly (from $468 billion). If they do nothing, then, House Republicans will prompt the writing of headlines that say, “GOP Chooses Military Dismantlement Over Tax Increase.” A hard-bargaining president could tell John Boehner, You want to be a cartoon Republican and block all tax increases? Fine. Then I’ll be a cartoon Democrat and allow a big fat cut in Pentagon spending. I’d rather not do that. But it’s your choice, pal.

Perhaps you’re wondering how it came to pass that the sequester’s automatic cuts for 2014, which were supposed to be divided evenly between defense and domestic discretionary spending, ended up encompassing nothing but defense spending. The short answer is that, through a complicated set of circumstances involving, among other factors, the fiscal cliff deal, the continuing resolution that resolved the government shutdown, and the 2011 Budget Control Act, the cuts to domestic spending ended up getting front-loaded in 2013, whereas the Pentagon cuts were not. (For a lengthier explanation, read this paper by the Center on Budget and Policy Priorities (CBPP), or this account by Kevin Drum of Mother Jones.)

The social cost of accelerating domestic cuts has been very high, which is why Democrats, quite appropriately, are very anxious to reverse them. And it should be remembered that keeping spending flat from one year to the next is a “cut” when you account for inflation and any population increase. Moreover, most budget analysts would argue that any cut relative to the funding level previously enacted by Congress must be judged a cut. That’s why the CBPP paper cited above, and also this one by the Center for American Progress (CAP), urge readers not to think of the 2014 sequester as sparing domestic discretionary spending. In a phone conversation in which he guided me, patiently, through the numbers, CAP’s Michael Linden urged the same.

But it’s a matter of simple arithmetic that the number of dollars spent on domestic discretionary programs would not change under the 2014 sequester. (If anything, it would increase very slightly.) Meanwhile, the number of dollars spend on military programs would change a lot. That makes the conflict between Democrats and Republicans an illustration of what, at the Pentagon, they call “asymmetrical warfare,” with Democrats in the unaccustomed role of superior power.

It may be that Obama and congressional Democrats will, in the end, decide that restoring spending that was sliced indiscriminately under the 2013 sequester is a higher political priority than raising taxes. (Contrary to popular stereotype, Democrats care not only about the domestic cuts but also, at least a little, about the Pentagon cuts.) Raising spending would of course increase the deficit, but no rational person should judge that much of a worry, at least for the short term. That’s because, as Furman noted, the deficit has, over the past four years, already come down faster, as a proportion of Gross Domestic Product, than at any point in history except during the demobilization period after World War II. Almost half of that decrease occurred just during the past fiscal year. Indeed, the deficit has come down so fast so quickly that further accelerating this reduction through additional spending cuts risks disrupting what little economic recovery the U.S. has experienced since the Great Recession formally ended in 2009.

If reversing sequestration is the deal Democrats want, they’d be foolish to deal away a tax increase at the outset. They are holding a much, much stronger hand than they were before the 2013 sequestration cuts took effect. They have the leverage this time, not a GOP whose approval ratings have dropped to historic lows. They need to act that way. And if they play it really smart they can cancel sequestration and get their tax increase, too.