At State Dinner, No Shortage of Opinions From Koch The Obama administration is not done hearing from former Mayor Edward I. Koch. Mr. Koch, after a very public break with the president last fall over his Israel policy and then an equally enthusiastic return to the fold, was a guest at Wednesday night's White House state dinner, along with Prime Minister David Cameron and his wife, Samantha; George Clooney; Anna Wintour; and a host of other politicians and celebrities. But just because Mr. Koch is back in the family doesn't mean he'll keep his opinions to himself. One of Mr. Koch's dinner table companions was Nancy-Ann DeParle, the president's deputy chief of staff for policy. "She said to me, "If you have any good ideas, send them on,"" he said, adding, "She doesn't know what she has in store for her." Mr. Koch said he had several thoughts, for instance, on the administration's natural gas policy, and since the secretary of energy, Steven Chu, has not responded to his correspondence, he said, Ms. DeParle will be his next target. Though he may remain a feisty interlocutor, however, Mr. Koch is definitely back in Camp Obama. He defected briefly last year, when he endorsed a Republican candidate, Bob Turner, in a Congressional race that Mr. Koch sought to frame as a referendum on Mr. Obama's Israel policy. After Mr. Obama met with Mr. Koch in private in September, though, Mr. Koch declared that he would support the president's reelection. On Thursday morning, in a phone interview on his way back from Washington, Mr. Koch said he thought Mr. Obama's chances looked very good. "He is on his own worthy of support and re-election," he said, "but the Republicans have made it much easier." In any case, he said, playing hard to get had seared him into the president's mind. Mr. Koch said he never took it for granted that anyone would recognize him. "The first thing I say to somebody when I meet them is, "I'm Ed Koch," even if it is my cousin," he said. But on Wednesday, when he approached the president, before he could say anything, Mr. Obama immediately said, ""You look terrific," and I said, "And you look even better,"" he recalled. The president then turned and introduced him to Mr. Cameron, who "flabbergasted" Mr. Koch, the former mayor said, by telling him that he had studied his mayoralty in school. Mr. Koch described Michelle Obama and Mr. Cameron's wife, Samantha, as "really beautiful women," but said he was most taken by a painting of Jacqueline Kennedy. "She just dominated the room," Mr. Koch said. It was breathtaking. Mr. Koch, who took as his date Diane Coffey, the chief of staff in his mayoral administration, said he conversed with Justice Antonin Scalia - a "charming guy" - as well as Senator Charles Schumer and his wife, Iris Weinshall, a former New York City transportation commissioner. (Mr. Koch said he suggested Ms. Weinshall reprise that role under a new mayoral administration. "I think she said, "No, thanks,"" he said.) Over the dinner of halibut and bison Wellington, Mr. Koch said he reminisced with Jane Holl Lute, a deputy secretary of homeland security, about their shared hometown of Newark, and chatted with Sally Susman, the finance chairwoman for the campaign of Mr. Koch's favored mayoral candidate, the City Council speaker, Christine C. Quinn. Ms. Susman's father, Louis B. Susman, is the ambassador to the United Kingdom. Mr. Koch also said he spoke with the secretary of state, Hillary Clinton, and encouraged her to run for president in 2016. "I said, "Everybody's running you for president again - count me in!"" he said. And there were other people there who applauded. He praised the food, and said he saved the menu for his archives at La Guardia Community College. His only disappointment, he said, was the entertainment - John Legend and the British group Mumford & Sons - which he said was not exactly to his taste. "If they had had Joan Baez, I would have been in ecstasy," he said.