"Changing their calculus," the president said of Iran, "is very difficult, even though this is painful for them and we are beginning to see rumblings in Iran that they are surprised by how successful we've been. That doesn't mean that they aren't working actively to get around it. But the costs of the sanctions are going to be higher than Iran would have anticipated six months ago, even three months ago."

"It may be that their ideological commitment to nuclear weapons is such that they're not making a simple cost-benefit analysis on this issue," Obama said. If Iran's "national pride" drives their policy, "then they will bear the costs of that." The president said he would use "all options available to us to prevent a nuclear arms race in the region and to prevent a nuclear-armed Iran" -- the euphemism for military strikes.

A few days ago, Iran's president, Mahmoud Ahmadinejad, said on state television that he was ready to meet Obama "face to face" in a televised debate: "man-to-man -- free and in the presence of media -- to put the issues of the world on the table." Obama said he'd be willing to consider bilateral meetings so long as allies were on board and nuclear issues were front and center. On Tuesday, Iran's foreign minister called for "transparent" discussions between the two nations.

Obama's theory of the case for preventing Iran's proliferation arises from two central premises. One, by engaging Iran, the United States would no longer be seen as the aggressor. "It wasn't initiated because we were naive about it," Obama said. "It was to send a message to the world community that if they were acting in a reasonable way, we were prepared to work with them."

Secondly, the U.S. would isolate Iran by making the concept of nonproliferation "an international norm and value." That gives the United States "the moral high ground when we argue that Iran, too, has to meet its international obligations." China and Russia, which had developed significant economic and political ties to Iran, had to be convinced that it was in their long-term interests to dissolve those ties given evidence that Iran was proliferating. Obama wanted to give the two countries a better offer: "Leverage," he said.

For economic sanctions, leveraging Russia "was the only way that we could ever get China to go along with the same thing." The resulting sanctions "are as tough as anything that's even been in place," Obama said, noting that the European Union and the U.S. had layered sanctions on top of what the United Nations decided earlier this year to impose. Iran has a way out, he said. There is a "clear path."

Obama said this even as administration officials fanned out across the world in an effort to build support for U.S., EU, and UN sanctions, and a day after the U.S. government imposed its first penalties on companies that did business with Iran under the new sanctions regime.