WASHINGTON — Niccolo Machiavelli, the 16th-century political realist and schemer, would relish the intricate calculations the three leading Democratic presidential candidates are required to make.

Hillary Clinton, Barack Obama and John Edwards need to do two things simultaneously: persuade the intensely antiwar majority in the Democratic Party that they despise President Bush’s Iraq policies, and demonstrate that they would be resolute in dealing with America’s foreign foes. Over the last week, their foreign policy dance has produced some revealing moments.

If you talk to members of Team Clinton, you quickly understand that her experience — both in the Senate and in the White House as a genuine governing partner with her husband — is their trump card against Obama. He may move Democratic crowds to tears and cheers, but Clinton would know what to do and how to do it from the moment she walked into the Oval Office.

Suggesting that this argument could get a hearing from Democrats, a Pew Research Center survey in mid-April gave Clinton a seemingly impregnable 39 percent to 5 percent advantage over Obama as the candidate having the “best experience” to be president. Most Democratic foreign policy gurus argue that among the party’s top three, Clinton has the most fully thought-through approach to international affairs.

That’s why there was glee in Clinton circles over Obama’s answer in last Thursday’s Democratic debate in South Carolina to a question about his likely response to simultaneous terrorist attacks on two American cities. Obama gave a 205-word reply without mentioning retaliation.

Edwards, who spoke next, could not wait to say that he would “act swiftly and strongly to hold them responsible for that.” And Clinton relished driving her toughness home. “I think a president must move as swiftly as is prudent to retaliate,” she declared. “I believe we should quickly respond.”

Obama, seeing the threat immediately, doubled back in response to a later, unrelated question to endorse “intelligently using our military and, in some cases, lethal force to take out terrorists.” But he had already given the Clintonites their opening, and they pressed their advantage over the weekend.

Yet it’s not clear how well toughness will sell among Democratic primary voters who are overwhelmingly and intensely critical of the Iraq war. Here, Obama, having opposed the war from the beginning, has an obvious advantage over Clinton because of her vote to authorize force in 2002 and despite her efforts to explain it.

Speaking before the California Democratic State Convention over the weekend, Obama could not resist an indirect dig at Clinton. “We’ve seen,” he said, “how a foreign policy based on bluster and bombast can lead us into a war that should’ve never been authorized and never been waged.”

Obama, however, faces risks on his other flank from Edwards, who renounced his own vote in favor of force and now displays the fervor of a born-again war opponent. With Obama and Clinton confronting the possibility that they may have to vote for compromise language on an Iraq supplemental appropriations bill, Edwards challenged Congress (and by extension his rivals) “to stand firm and strong” on Iraq.

“If the president vetoes this bill, they should send him back another bill with a timetable for withdrawal,” Edwards told the California convention. “If he vetoes that, they should send him another one back with a timetable for withdrawal.” Edwards thus raised the prospect that for Obama and Clinton, their obligations as members of the Senate’s narrow Democratic majority may conflict with the imperatives of their presidential candidacies.

Obama faces the knottiest political problems of the top three. He is being challenged on his right (on experience and toughness) and his left (with antiwar Democrats fearing he will embrace establishmentarian views). His detailed foreign policy speech last week received generally favorable reviews from the foreign affairs powers that be but drew criticism from the left, especially for his refusal to renounce the use of military force against Iran.

By contrast, Edwards has decisively thrown in his lot with the party’s antiwar wing, while Clinton is distinguishing herself not only from President Bush, but also from Obama by embracing a brand of tough-minded realism.

The upside for Obama is that circumstances are forcing him to define a new center of gravity on foreign policy in Democratic politics. If he succeeds, the rewards he reaps could be as great as the risks he now faces.

E.J. Dionne’s e-mail address is postchat(at symbol)aol.com.

© 2007, Washington Post Writers Group

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