"The State Department ought to take lessons from me," boasts Duke Zeibert. "I've settled more political, diplomatic and sports battles than you can imagine."

If any Washington institution enjoys true bipartisan support, it is Duke Zeibert's Restaurant, four blocks from the White House. Every President since Harry Truman—with the exception of Jimmy Carter, who sent son Jeff with an autographed picture—has dined on its hefty steaks and chops, corned beef and cabbage, plump crab cakes and traditional Jewish dishes. LBJ used to insist on a New York strip sirloin medium rare. "He was as bossy and demanding as he was on the Hill," Duke says. Nixon favored Hungarian goulash. Ford was a roast beef man.

Zeibert packs in 800 to 1,000 at lunch and 350 at dinner every day, but only big shots are seated in the front room. "My best night," Duke recalls, "was when Jimmy Hoffa was on one side of the room, George Meany on the other and J. Edgar Hoover right in the middle. You can't plan something like that." The mix usually includes showbiz types like Jerry Lewis and Ed McMahon, media celebs from Art Buchwald to ABC's Frank Reynolds, a near quorum from Congress and, for spice, some outcasts. Duke remains friendly with onetime Capitol Hill mistress Elizabeth Ray. "She's a poor, helpless child," he sympathizes. "A black kid in the ghetto gets out through sports. Liz wanted out, and that was her only talent."

Duke's pecking order places athletes above senators. When Vince Lombardi coached the Redskins, he was positioned where autograph seekers could get to him easily. Approached one day by a small boy, he signed a menu and handed it to the child. "I just wanted the catsup," the boy said. For working sessions with his coaches, Lombardi was given a back room. Under his successor, George Allen, the room became known as "Allen's Alley," and currently it's "Pardee's Parlor" for head coach Jack Pardee.

The 69-year-old Zeibert talks a good game, but seldom plays any (except occasional golf). When Gerald Ford asked him about his game, Zeibert quipped, "Mr. President, I'm dressing like Ben Hogan but playing like Ben-Gurion." But after visiting the Pritikin Longevity Center in Santa Monica, Calif, last fall ("I checked the place out with McGovern; his wife, Eleanor, had been there"), Duke shed 43 pounds and a five-pack-a-day cigarette habit. "I feel reborn," he exults. "I used to have angina, and for 16 years took insulin for my diabetes. Now I walk three miles a day and work out at the YMCA. It doubled my sex life too." (A longtime customer teases, "Now he does it twice a year.") In 1964 Zeibert was divorced from his third wife, with whom he had three children. "That was a real marriage," he says. "It lasted 20 years and the others just a minute."

The son of a painting contractor from Troy, N.Y., David George Zeibert started as a Borscht Belt busboy, was a movie extra ("It was the Depression—you did anything to eat") and found his niche at Fan and Bill's Restaurant in Miami Beach. His uncanny skill at remembering names made him the most popular headwaiter in town. "I was fantastic, really," he maintains. "I took a course in mnemonics—a memorization technique—and could meet a guy and call him by his name 25 years later."

When Fan and Bill's moved to Washington in 1941, Zeibert went along. Nine years later he opened his own place. "Mine was the first New York-style restaurant in this town," he brags. "If you didn't eat here, you were camping out."

Zeibert has long talked about writing an anecdotal cookbook to celebrate his mother's Jewish dishes and his famous customers' favorites: "For Muhammad Ali, it's crown roast of lamb; for Senator Javits, hamburger a la Duke." Although House Speaker Tip O'Neill ate at Duke's four nights a week for 25 years, he still can't decide which specialty he likes best. "That Tip," Zeibert says fondly, "he's a .400 batter with a knife and fork."

This summer after 30 years at a prime location off Connecticut Avenue, Duke will be forced to relocate to make way for an office building. He has postponed choosing another site. "Donnie Graham [publisher of the Washington Post] wants me to move into his new building," Duke reports, "but that is a year off. Who knows, maybe I'll find, after 50 years in this business, I like it on the outside."