The more high-profile Republicans repudiate Trump, the weaker he looks as a general-election candidate. But in the race to win over independent and Republican voters, an endorsement from someone with as much name recognition as Henry Kissinger, a former secretary of state to Richard Nixon and Gerald Ford, would be even more powerful.

"The messenger matters," said Elizabeth Saunders, a political science professor at George Washington University. "In general it's surprising to see high-profile Republicans cross the aisle to endorse a Democrat, and the more prominent the person making an endorsement, the more powerful the effect."​ If Kissinger, Rice, Baker or Shultz endorse​d​ Clinton, that would be "a big deal," Saunders noted,​ since it would be "a Republican at the very highest and most recognized level, a former Secretary of State, crossing the aisle to endorse."

There are plenty of reasons Republican foreign-policy experts might prefer Clinton to Trump. As a former secretary of state, Clinton has far more foreign-policy experience. On top of that, Trump has broken with Republican consensus by threatening to upend U.S. participation in NATO and rip up international trade deals. His presidency could dramatically alter the way America engages with the rest of the world. That unconventional stand creates an opportunity for Clinton.

“Trump represents a strong break with foreign policy tradition, and I think Secretary Clinton is trying to capitalize on that,” said Nora Bensahel, a distinguished scholar in residence at American University’s School of International Service. “She’s trying to appeal to Independents and Republicans who are on the fence about Trump and have questions about what his judgment as commander-in-chief would look like.”

Clinton has already won outright endorsements from some prominent members of the Republican foreign-policy establishment. Brent Scowcroft, a national security adviser to Ford and George H.W. Bush, and Richard Armitage, a deputy secretary of state under George W. Bush, have publicly declared they plan to support Clinton over Trump. The Clinton campaign recently put out an ad that features conservatives questioning Trump’s ability to serve as commander-in-chief.

The focus on national-security risks alienating progressive voters wary of Clinton’s reputation as a foreign-policy hawk more likely to support military intervention abroad than President Obama and other Democrats. Chants of “No more war!” rung out inside the Wells Fargo Center when former Secretary of Defense Leon Panetta and retired General John Allen spoke in support of Clinton at the Democratic National Convention.

“Henry Kissinger is an architect of war,” said Winnie Wong, a co-founder of The People for Bernie Sanders. “That Hillary Clinton is purportedly courting an endorsement from him speaks volumes about her future foreign-policy plans for the United States. Progressives want peace. This is not peace.”