Mr. Obama never wanted to be an ordinary politician — there was a time when Mrs. Obama could barely use that noun to describe her husband — and his advisers resist the idea that he has succumbed to standard Washington practice. Some donors and aides give an “if only” laugh at the idea that the couple now follows political ritual more closely: this is a president who still has not had Bill and Hillary Rodham Clinton to dinner but holds lunches to discuss moral philosophy with the fellow Nobel laureate Elie Wiesel.

“He thinks about destiny in human terms,” Mr. Wiesel said in an interview.

Still, others say the Obamas have become more relaxed schmoozers, more at ease with the porous line between the political and social, more willing to reveal themselves. They have recently begun inviting more outsiders into their private living quarters, including Mr. Kushner, Steven Spielberg and Daniel Day-Lewis at the “Lincoln” dinner. At a dinner in late November to thank top campaign fund-raisers, the first couple was like a bride and groom, bantering and traveling from table to table to accept congratulations and good wishes for the years ahead, making sly jokes that guests would not repeat for publication.

Even Mr. Obama’s speech has changed a bit, close observers say. Though he still disdains Washington, he often sounds less like a disapproving outsider and more like a participant.