Both Mr. Kagan and his brother are taking considerable pains to describe their advocacy as broadly bipartisan. “The urgent priority is to unite internationalists on both sides of the spectrum,” said Fred Kagan, while his brother, Robert, mentioned his briefing of a bipartisan congressional delegation at Davos and his good relations with top White House officials, including the national security adviser, Susan E. Rice. (Their father apparently did not get the memo, calling Mr. Obama’s speech “pathetic” and saying of the president, “We should not underestimate the possibility of extraordinary ignorance.”)

But Exhibit A for what Robert Kagan describes as his “mainstream” view of American force is his relationship with former Secretary of State Hillary Rodham Clinton, who remains the vessel into which many interventionists are pouring their hopes. Mr. Kagan pointed out that he had recently attended a dinner of foreign-policy experts at which Mrs. Clinton was the guest of honor, and that he had served on her bipartisan group of foreign-policy heavy hitters at the State Department, where his wife worked as her spokeswoman.

“I feel comfortable with her on foreign policy,” Mr. Kagan said, adding that the next step after Mr. Obama’s more realist approach “could theoretically be whatever Hillary brings to the table” if elected president. “If she pursues a policy which we think she will pursue,” he added, “it’s something that might have been called neocon, but clearly her supporters are not going to call it that; they are going to call it something else.”

Whatever it is called, it is a dominant strain in the Kagan clan. As a boy, Robert accompanied his father to the faculty club on the Cornell campus, where high-level conversation made an impression. (So did the philosopher Allan Bloom, the author of the conservative manifesto “The Closing of the American Mind,” who accidentally put out a cigar in his hand at a poker game.)

Fred Kagan, more cerebral than Robert, went on to become a West Point professor, and his paper for the American Enterprise Institute, “Choosing Victory, a Plan for Success in Iraq,” served as the intellectual basis for the 2007 troop increase, the so-called surge. Later, he went on to spend months with his wife, Kimberly, now president of the Institute for the Study of War, in Afghanistan, poring over Taliban correspondence at the invitation of Gen. David H. Petraeus.

Robert Kagan, armed with graduate degrees in public policy and history, cut his teeth working in the Reagan administration. It was during that time that he attended a party thrown by Ms. Nuland, a disarmingly charming and talented young Foreign Service officer. The two had friends and a hometown in common, as she, too, had a famous Yale professor for a father, Sherwin Nuland, the author of “How We Die.”

They had some bad dates and then a good one at a Cuban restaurant where, Ms. Nuland said, they fell in love “talking about democracy and the role of America in the world.” The couple married in 1987. Ms. Nuland climbed the diplomatic ladder, serving as chief of staff to Deputy Secretary of State Strobe Talbott — now her husband’s boss at the Brookings Institution — and in the Bush administration, as a key foreign-policy adviser to Vice President Dick Cheney and ambassador to NATO. When asked about her husband, Ms. Nuland recites a “he’s him and I’m me” mantra. Mr. Kagan offers that “with any marriage where do you leave off and they begin?”