Two hundred and fifty U.S. Marines in Australia doesn’t sound threatening.

But President Obama’s decision to deploy the Marines — rising to 2,500 — on a permanent basis in Darwin from next summer on is a powerful symbol for Beijing, which in the past few days has been told to act like a “grown-up” by the U.S. leader.

I’m all for playing hardball with China, and Obama probably thinks that talking tough will play well at home. “The United States is a Pacific power and we’re here to stay,” he told Australians in remarks that were actually designed for an assertive China.

But timing is everything in foreign policy, and right now America needs the Chinese more than they need us. So the rhetorical shift could easily backfire on the White House, which wants to enlist Chinese support in tightening sanctions on Iran — probably the administration’s biggest foreign-policy headache.

Even before Obama’s announcement on the troops for Australia, China was reticent about helping to curb Iran’s nuclear program. Beijing has become Iran’s top trading partner and highlights diplomatic options rather than international attempts to isolate Iran via the sanctions route.

At an Atlantic Council event last week, John Garver of the Georgia Institute of Technology said that China could see a strategic advantage if U.S. soldiers remained tied up in the Persian Gulf, which would mean they would have less time to spend in the Western Pacific.

Chinese leaders are convinced that the U.S. is engaged in containing China. They will not have been reassured by Obama’s stance this week.

Of course, it could be that the administration has concluded that China is unlikely to cooperate for geostrategic reasons, so there is nothing to lose by staking out a tough position now and reassuring regional allies. But confirming Chinese fears about U.S. encirclement will only further strain a relationship already marked by misunderstanding and mistrust.