WASHINGTON—After weeks of internal debate on how to respond to uprisings in the Arab world, the Obama administration is settling on a Middle East strategy: help keep longtime allies who are willing to reform in power, even if that means the full democratic demands of their newly emboldened citizens might have to wait. Instead of pushing for immediate regime change—as it did to varying degrees in Egypt and now Libya—the U.S. is urging protesters from Bahrain to Morocco to work with existing rulers toward what some officials and diplomats are now calling “regime alteration.” The approach has emerged amid furious lobbying of the administration by Arab governments, who were alarmed that President Barack Obama had abandoned Egyptian President Hosni Mubarak and worried that, if the U.S. did the same to the beleaguered king of Bahrain, a chain of revolts could sweep them from power, too, and further upend the region’s stability. The strategy also comes in the face of domestic U.S. criticism that the administration sent mixed messages at first in Egypt, tentatively backing Mr. Mubarak before deciding to throw its full support behind the protesters demanding his ouster. Likewise in Bahrain, the U.S. decision to throw a lifeline to the ruling family came after sharp criticism of its handling of protests … >>>