“Was Bush right?” scoffed one Obama adviser who spoke on the condition of anonymity. “Give me a break. How many democratic transformations like this took place when he was in office?”

Several, actually, in Ukraine, Georgia, Lebanon and Kyrgyzstan, where popular risings also toppled entrenched ruling systems. But later events in those countries also showed that such first steps did not necessarily point in a straight line to lasting Jeffersonian democracy. Similarly, the change in Egypt has only begun, as Mr. Obama pointed out on Friday. Its final destination is still very much up in the air…

Aides to Mr. Obama said he can make progress where Mr. Bush faltered because the current president has made reaching out to the Muslim world a priority and has de-emphasized the idea that the fight against terrorism means a war on Islam. While Mr. Bush also sent such messages, Obama aides said the baggage of Iraq and Guantánamo Bay undercut the impact.

“We do not make this about us,” said one senior administration official, who was not authorized to be identified. “We very carefully say this is about the people. We’re on the sidelines, we never talk about our values, we talk about universal values. Does that create space for these things to happen?” Hopefully so, the official said.