Johnny Cash strode through an ebullient throng with a steady gait, a solid handshake for all, and his redhaired son John tugging him by the arm. As hundreds of guests in the Kennedy Center Atrium swarmed around him, the black-suited country singer stepped onto a cushioned bench and delivered his now-famous line, "Hello, I'm Johnny Cash."

His appearance with his wife, June Carter Cash, last night was the highlight of a cocktail party preceding "Johnny Cash's America," a 75-minute concert that celebrated America's musical history and raised funds for the Lombardi Cancer Research Center at Georgetown University.

Cash's wife said the musician suffered a blood clot in one leg several days ago and now has 30 stitches, although no impairment was evident last night. "His knee hurts only when he stands on it," she said.

As Cash walked out of the party--past an elegant display of poached salmon and goose liver pa te'--he was again besieged by admirers who shook his hand, patted his shoulder and tugged at his clothes. He stopped briefly to shake hands with Sen. Robert C. Byrd (D-W.Va.), seated at a table near the door, then quickly disappeared to prepare for his show.

Earlier during the party, Byrd, a fiddler, said he performed with Cash two years ago at a state fair in West Virginia. "He asked me to play with him tonight," said the senator, who refused because of a recent death in the family.

House Speaker Thomas P. (Tip) O'Neill (D-Mass.), who has known the Cashes for years, said he plans to participate in this afternoon's Lombardi Memorial Golf and Tennis Tournament, an annual fund-raising event for the Research Center. "I'm the world's worst golfer," he said.

"I've been associated with the tournament since it started," O'Neill said, "because I liked and respected Vince Lombardi , who was a good leader of men and a great athlete." Lombardi, who coached the Green Bay Packers and the Washington Redskins, died of cancer in 1970 at Georgetown University Hospital.

The first tournament 11 years ago raised $5,000, O'Neill said. This year, the concert--for which tickets cost $20 to $1,500--raised $60,000 and the tournament raised about $300,000, according to Tom Wheeler, chairman of the event and president of National Cable TV Association.

The preconcert party was given by Ralph P. Davidson, chairman of the board of Time Inc., Gerald M. Levin, vice president of Time's video group, and James O. Heyworth, president of Home Box Office Inc.

"HBO picked up the tab," said Tom Wheeler, "so every dollar raised is going directly to the Research Center." HBO, he added, was taping "Johnny Cash's America" and would air it in August.

Cohost Ralph Davidson said of the fund-raiser, "I think this is what corporate America ought to be doing more of--using some of its influence and money to make American communities better."