Russia, whose president, Dmitry Medvedev, will meet Obama at the United Nations next week, is key to any such effort. So far, it has resisted further sanctions on Iran, which it supplies with weapons and other technology.
If Obama's move was designed to nudge Russia, early signs Thursday weren't encouraging.
Russian Foreign Minister Sergey Lavrov said in a speech before Obama's missile-defense announcement that Moscow will continue to oppose any new sanctions over Iran's nuclear program.
Medvedev, however, said after the announcement that Obama's action was a "responsible move."
Until now — leaving aside domestic issues with foreign policy implications, such as the treatment of terror detainees — Obama's foreign policy hasn't radically departed from that of his predecessor, though the rhetoric has been much different.
He has talked more about engaging adversaries, though no presidential summits have materialized. He has continued Bush's gradual withdrawal from Iraq and added troops to Afghanistan.
Pushing a so-called "reset" button in the USA's relationship with Russia has yielded little that is tangible. Polls in various countries show that Obama is far more popular abroad than Bush is, but that popularity has yet to translate into visibly better cooperation with U.S. policy goals.
Christian Brose, who was a speechwriter for Bush Secretary of State Condoleezza Rice, wrote recently on foreignpolicy.com: "Our NATO allies have passed on sending more troops to Afghanistan and on lifting restrictions on those already there ... India and China don't share any of Obama's enthusiasm for a climate change deal. ... Pakistan is still dysfunctional and supporting terrorism. Iran and North Korea are all middle fingers and no unclenched fists. ... Rarely has a U.S. administration been so well-liked, so eager to engage with others, and had so little to show for it."
Obama officials disagree, of course, but it's not just former Bush officials who hold that view: In July, Columbia University professor and liberal blogger Lincoln Mitchell wrote a post entitled, "Why Obama's Foreign Policy Looks So Much Like Bush's." He previously was a Democratic consultant.
Republicans, including Obama's 2008 opponent, Sen. John McCain of Arizona, have supported many, though not all, of the new president's foreign policy moves. On Thursday, though, they erupted in a chorus of criticism.
McCain called the decision "seriously misguided," while Florida's Ileana Ros-Lehtinen, ranking Republican on the House Foreign Affairs Committee, dubbed it "a policy of appeasement."
Marc Thiessen, a former Bush speechwriter now at the Hoover Institution, said the "disastrous decision" sends "a signal of weakness to Tehran ... and a terrible signal to Russia, that they can bully us into abandoning our friends in what they consider their sphere of influence."
The partisan uproar came despite the endorsement of the move by Gates, who was Bush's secretary of Defense when the deals with Poland and the Czech Republic were finished last year and who holds the same job for Obama.
"This new approach provides a better missile-defense capability for our forces in Europe, for our European allies and eventually for our homeland than the program I recommended almost three years ago," Gates told reporters at the Pentagon after Obama spoke.