Rosalynn Carter, who with her husband has spent the spring getting acquainted with Washington's influential, made a pilgrimage yesterday to yet another bastion of power, the 700-member Congressional Club.

The occasion was the annual First Lady's Breakfast, a tradition almost as old as the 69-year-old club and an event a President's wife dare not miss if she knows what's good for the President (as John Kennedy did in 1963 when he substituted for his wife, Jacequeline).

I'm really overwhelmed," Rosalynn Carter told the record crowd of 1,000 at the Shorham Americana which included spouses of the Vice President, Supreme Court Justices, the Cabinet, U.S. senators and representatives and actress Elizabeth Taylor, who in her remote corner of the room was as besieged by autograph-hounds as the First Lady.

Taylor's reservation, through her hostess, Jermaine Magnuson of Washington, had reached the committee late and cost her a "choice" table, according to cochairman Mae Guyer of Ohio.

And compared to her White House predecessors, Rosalynn Carter's acceptance had taken longer than Guyer thought customary. "She's not been a congressional wife, so she doesn't know anything about the club," said Guyer, who told of calling the White House in January "several times . . . We were getting anxious to hear."

The hotel's Regency Ballroom was decorated with paper versions of Georgia's state flower, the Cherokee rose, against a bright green-and-white color scheme. "Carter campaign colors," the First Lady noted with satisfaction.

Introduced by club president Doris McClory of Illinois, the First Lady presented checks for $500 each to the D.C. Chapter of Recordings for the Blind and the Mental Health Program of the District.In return, she received a needlepoint rendition of the White House, a serenade by singer Tony Bennett and protection from inquiring reporters at a pre-breakfast VIP reception.

In 1974, reporters attending the reception questioned then-First Lady Pat Nixon about Watergate and, according to Guyer, "We were very embarrassed about that." Since then, the press has been barred from the reception in an effort to protect the First Lady from being "put on the spot."

Yesterday's breakfast, at $12.50 a ticket, cost $2.50 less than in 1976 and was made possible because "We had a little extra left over from last year," said Guyer. "We don't expect to make money."