Jimmy Carter's chief of staff sat next to Nancy Reagan, and Ed Meese, Ronald Reagan's transition chief, laughed over dinner with White House counsel Lloyd Cutler. Party differences, at least for an evening, seemed forgotten at a dinner for the Reagans given last night by Washington Post Co. chairman Katherine Graham.

"There was a great sense of people wishing the new team good luck," said Jack Watson, who'll be White House chief of staff for not even two more months.

"I felt a sense of the country as a whole, as distinct from party differences," said economist Alan Greenspan. "What struck me is that this differs, in a sense, from what one sees in other countries. There's an extra unity."

In her after-dinner toast, Graham told the Reagans that she was looking forward to 1981, and hoped that everyone in the room would come back in a year. f

"It's on the calendar already," said Nancy Reynolds, an aide to Nancy Reagan.

Guests began arriving at Graham's R Street home at about 7:30 p.m. Among the first was former secretary of state Henry Kissinger, who bounced out of his limousine to noisily greet Vernon Jordan, president of the National Urban League. "This proves anybody can get invited to these things," Kissinger wisecracked to Jordan.

And then, when asked why he wasn't included in the batch of Cabinet nominations announced yesterday, Kissinger replied: "I wanted an aristocratic title. If they had made me a duke . . ."

The dinner menu included sauteed veal with mushrooms, carrots and and onions and for dessert, a marrons puree with whipped cream. There were six round tables of 10 each, lit by candles and covered with linen. White and pink lilies were at the centers, and also spread through the house.

Most of the political talk centered on speculation that Alexander Haig would be secretary of state. But Allen Neuharth, of Gannett, talked with Joseph Alsop during dinner about a new Theodore Roosevelt biography, and Watson talked with Nancy Reagan about horseback riding as well as what to expect at the White House.

Still, Haig dominated. But when might a secretary of state be named?

"Oh," said Meese cryptically, "sometime soon."

The dinners 60-plus guest list was balanced to include media executives, social-establishment Washington, both parties on Capitol Hill, and incoming and outgoing administration members.

From the new administration came James Baker, Reagan's chief of staff; William Casey, named yesterday as CIA director; Meese, counselor to the president-elect; Rep. David Stockman (R-Mich.), designated yesterday as director of the Office of Management and Budget; and Michael Deaver, aide to the president-elect.

The outgoing administration was represented by Watson, who is also director of the transition effort from the Carter side, and Cutler.

From Capitol Hill came Rep. Millicent Fenwick (R-N.J.) and senators Nancy Kassebaum (R-Kan.), Charles McC. Mathias (R-Md.), Sam Nunn (D-Ga.) and Gary Hart (D-Colo.).

From the press: James Shepley, chairman of the board of the Washington Star Co.; Richard Munro, president of Time Inc.; Peter Derow, chairman of the board of Newsweek Inc.; John Sweet, chairman of the board of U.S. News and World Report; Edward Walker Estlow, president of the E.Q. Scripps Co.; Neuharth, president and chairman of the Garnett Co. Inc.; Alvah Chapman, president and chief executive officer of Knight-Ridder Newspapers; Stanton Cook, chairman and publisher of the Chicago Tribune; Warren Buffett, chairman of Berkshire Hathoway, Inc. and a major stockholder and director of the Washington Post Co.

Also attending were author and retired columnist Alsop, current columnist George Will and former transportation secretary William Coleman Jr.

Since Nov. 4, the Reagans have been the most sought-after dinner guests in Washington, New York and Los Angeles. Three weeks ago, Will entertained them at his Chevy Chase home at one of the season's most talked-about parties. A week and a half ago, they were honored at a mammoth downtown Los Angeles reception given jointly by the volunteer group called the Amazing Blue Ribbon and the Times Mirror Co., which publishes the Los Angeles Times.

This week, New York philanthropist and hostess Brooke Astor had a party for the couple in her Park Avenue apartment; major business and publishing executives attended.

Before that, Reagan friends Alfred and Betsy Bloomingdale gave the couple a black-tie dinner party for 28 in California, and Sen. Howard Baker (D-Tenn.) held yet another dinner party in their honor on Capitol Hill.

The Reagans themselves began the entertainment marathon Nov. 18 with an F Street Club party for District of Columbia leaders. Judging from that and their other party appearances so far, they relish their new role as toasts of the three towns. At Brooke Astor's party earlier this week, they stayed nearly two hours past their scheduled departure time, and last night, said their goodbyes at 11:15 p.m. -- more than an hour after they were expected to leave.