‘‘The clock is ticking. We’re not going to allow Iran to perpetually engage in negotiations that lead nowhere,’’ Obama said in his last foreign policy debate with Republican presidential candidate Mitt Romney. ‘‘We have a sense of when they would get breakout capacity, which means that we would not be able to intervene in time to stop their nuclear program.’’

Syria’s widening conflict is another concern. More than 36,000 people have died in the last 20 months, as a brutal crackdown on dissent by President Bashar Assad’s regime has descended into a full-scale civil war. Obama has demanded Assad’s departure, yet has ruled out military assistance to the rebels or American military actions such as airstrikes or enforcing a no-fly zone over Syria.

Last week, in a significant shift in policy, the secretary of state demanded a major shakeup in the opposition’s ranks in the hopes of rallying Syrians behind the rebellion. However, Clinton’s spokeswoman, Victoria Nuland, reiterated Wednesday the administration still rejects the notion of providing weapons to anti-Assad fighters or any talk of armed intervention.

In other places, Obama’s engagement efforts may get another look. After some success with a rapidly liberalizing Myanmar, there are hopes for democratic reforms and human rights advances in Cuba and North Korea, among others.

But short of a rapid change in attitude from these governments, Obama’s options for a landmark breakthrough in U.S. diplomacy are limited. He won’t be able to reach out to Havana until it frees the jailed U.S. contractor Alan Gross, while Pyongyang will have to denuclearize if it wants better relations with America — steps neither regime has shown a willingness to entertain. The recent re-election of Venezuelan President Hugo Chavez has halted chances for now of any rapprochement between Washington and Caracas.

In Afghanistan, the president will seek to stick to NATO’s 2014 withdrawal date for most international troops, a central campaign promise. His administration has been trying unsuccessfully to jump-start peace negotiations between President Hamid Karzai’s Western-backed government and the Taliban. The so-called reconciliation effort relies heavily on America’s frustrating and unreliable ally Pakistan, where extremist groups such as al-Qaida and the Haqqani network will continue to face U.S. drone attacks.

Behind all the diplomatic efforts are larger questions of American geopolitical strategy. Obama had initial success improving U.S. relations with Russia, getting a nuclear arms-reduction pact in 2011, but has since seen America’s former Cold War foe frustrate U.S. missile defense plans and hopes of an international consensus on Syria. The president has continued to trumpet the benefits of his Russia ‘‘reset’’ policy but may take a firmer stance against Moscow if it refuses to show compromise.

For economic reasons, China policy is less likely to change. The world’s two biggest economies are deeply interdependent and, despite lingering disagreements over Beijing’s currency exchange rates and intellectual property infringement, neither side will want to do anything that threatens a trade war and jeopardizes China’s booming growth or America’s still-fragile jobs recovery.

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