Even after the strategy is fully implemented, he said, "the defense budget will still be larger than it was at the end of the Bush administration."
So it seemed a little odd when, an hour later, the second-ranking official in Obama's Pentagon presented what sounded like a rebuttal.
"You have, over the next four years, a reduction in total defense spending as rapid as any we experienced after Vietnam or after the Cold War," Deputy Defense Secretary Ashton Carter said.
The two statements weren't as contradictory as they sound. When Obama said the defense budget would continue to grow, he was talking about the Pentagon's core budget, not the extra costs of waging wars in places like Iraq and Afghanistan. When Carter said spending was about to plummet, he was talking mostly about war spending, plus the modest trims the administration proposes on future growth in the non-war budget.
But the contrast between the two statements - are we cutting, or are we growing? - reflected the underlying dilemma of Obama's desires on defense: He wants to have it both ways.
The president has been blunt in arguing that the nation's fiscal problems can't be solved unless military spending is reduced. To that end, he has imposed a cut of $487 billion in the core defense budget over the next 10 years, and threatened to cut more if needed.
But will the budget cuts leave enough, as Obama has promised, to enable the military not only to continue the fight against terrorism but also to increase the U.S. military presence in Asia and to defeat any conceivable adversary that arises?
The president has sought to lay out a global strategy on a shoestring, but it's a very large shoestring; that core budget will still amount to an average of about $560 billion a year for the next 10 years.
"It's not perfect," said Army Gen. Martin E. Dempsey, chairman of the Joint Chiefs. "There will be people who think it goes too far. Others will say it didn't go nearly far enough. That probably makes it about right for today."
That won't make it immune from sniping in an election year, though.
The two leading Republican candidates for president, Mitt Romney and Rick Santorum, immediately denounced Obama's proposal and reiterated their calls for significant increases in defense spending over the next 10 years.
But the issue divides the Republican Party between two kinds of hawks: defense hawks and budget hawks.
Public opinion polls, on the other hand, are less ambiguous: Most Americans oppose deep cuts in defense spending, but they divide on partisan lines. The Democrats and independents whose votes Obama needs for reelection are likely to applaud the careful cuts he has proposed.
Obama will be criticized over the coming weeks by Republican legislators for proposing cuts they consider too deep. But over time, the question will more likely be whether the president, acting in this election year, cut deeply enough.
Doyle McManus is a columnist for The Los Angeles Times. Readers may send him email at doyle.mcmanuslatimes.com.