One of the few areas of real disagreement in Monday’s debate between President Obama and his GOP rival, former Massachusetts Gov. Mitt Romney, was over the size of the defense budget. Romney said the Navy and Air Force had gotten too small and that Obama had abandoned the country’s longtime commitment to having a military large enough to fight two wars at once. Obama countered that the military’s needs evolved over time and that Romney wanted to spend $2 trillion on defense (over 10 years) that “the military is not asking for.”

The media (myself included) seized on Obama’s snarkiest comment of the evening, which came in response to Romney’s complaint about the Navy and the Air Force: “We also have fewer horses and bayonets, because the nature of our military’s changed. We have these things called aircraft carriers, where planes land on them. We have these ships that go underwater, nuclear submarines.”

But the thing Obama said that seemed to resonate most across the Twitterverse was an observation about the sheer magnitude of the defense budget. “We spend more on our military than the next 10 countries combined; China, Russia, France, the United Kingdom, you name it. The next 10,” Obama said.

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That’s true, but it also understates the case. The Peter G. Peterson Foundation, an advocacy group for a more fiscally responsible federal budget, noted Tuesday that the United States spends more than the next 13 countries combined. The chart above tells that story at a glance.

The foundation argued in an unbylined blog post Tuesday that the looming across-the-board cuts in defense (and domestic programs) aren’t the right way to go about slimming down the Pentagon. But it agreed with Obama that significant defense cuts are possible, provided they are consistent with a new strategic vision:

“Changes in the international security environment since the end of the Cold War, as well as the drawdowns in Iraq and Afghanistan, allow for a rethinking of the country’s global engagement strategy -- and could produce significant savings for the federal budget,” the foundation’s staff opined. “However, any changes in defense spending should be guided by a strategy that identifies the country’s interests, potential threats to those interests, and the best military and diplomatic methods for countering those threats. And that strategy should take account of our country’s military superiority, the difficulties of waging protracted land wars, and future threats to our security that come from non-state actors.”

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Follow Jon Healey on Twitter @jcahealey