BARI, Italy — For all the ambitious plans that President Joe Biden and his counterparts unfurled at the summit meeting that ended Saturday, the cold reality is that many of the leaders may not remain in office long enough to see them ripen.

A populist, far-right movement rippling through Europe and the U.S. threatens to unseat Biden and some of his closest allies, jeopardizing the deals forged over the past few days on Ukraine’s defense.