The forced withdrawal of Theodore C. Sorensen's nomination to be Director of Central Intelligence - the first defeat of Jimmy Carter's still-unborn presidency - was a painfully public display of Carter's limited influence on Capitol Hill.

Carter's associates tried quickly to minimize the political significance of Sorensen's withdrawal. It was argued that Sorensen's personal liabilities were substantial, so his rejection was not simply a slap at Carter.

But the President-elect did try to save Sorensen, with public statements of full support and with private telephone calls to key senators on the Intelligence Committee.

Perhaps the most revealing aspect of the entire tale was Carter's inability to convince at least four senators of his own party to give him and Sorensen the benefit of the doubt.

This could be an omen of the political realities in the first months of the Carter administration. The Democratic members of Congress - most of whom ran ahead of Carter in their home districts last fall - feel no special debt to the President-elect. And thus far he has not generated the kind of popular support that might convince the Congress he is too popular to take on.

Carter's unusually ardent courtship of Congress during the transition period suggests a realization that his position needs strengthening. His decision not to fight harder for Sorensen may be a sign of strategic political tractability.

And Sorensen obviously did pose a special set of problems. He had few enthusiastic supporters and many critics from all sides of the political arena.

Moreover, Sorensen's candid affidavits on behalf of Daniel Ellsberg and The New York Times in the Pentagon Papers case inflamed the powerful intelligence lobby on Capitol Hill - the same forces what routed Sen. Frank Church (D-Idaho) and other would-be reformers who sought to strengthen congressional control over the intelligence community last spring.

So Carter's defeat this time does not necessarily foreshadow a series of additional defeats in the future. But it does demonstrate his vulnerability.

And it leaves him with an enormous problem: who can he find to run the Central Intelligence Agency?

Several names circulated among well-placed speculators yesterday: Thomas L. Hughes, president of the Carnegie Endowment for Peace, who asked Carter not to consider him for the CIA post before Sorensen was picked; Burke Marshall, deputy dean of the Yale Law School and an assistant attorney general in the Kennedy administration; and Paul C. Warnke, Washington lawyer and former assistant secretary of defense, who has just turned down the directorship of the Arms Control and Disarmament Agency.

Another name mentioned was Gerard C. Smith, also a Washigton lawyer, who was the leader of the American delegation to the Strategic Arms Limitation Talks (SALT) in the early 1970s.

All four would fit the description of the type of person the President-elect, according to his press secretary, still seeks in a director of the CIA; "someone . . . from outside the intelligence community, someone with a degree of independence but with experience."

Several members of Washington's foreign policy establishment speculatted privately yesterday that Carter may also need a candidate for the job who will seem less than ideal to the right-wing elements in the Senate which avidly pressed the fight against Sorensen during the last week.

According to this theory, if Carter now names someone with a hawkish reputation to the CIA job, he would be conceding an important victory to the right at the very outset of his administration.

The conservatives have already pushed Carter hard on his choice of a Defense Secretary, though he resisted pressure against Harold Brown, the man he eventually picked for that job. Several sources speculated yesterday that the withdrawal of Sorensen's nomination may embolden the hawkish members of the national security community to press for a more hawkish figure at the CIA.

One of the Democratic senators quoted anonymously over the weekend as opposing Sorensen suggested that Carter needed a man like James R. Schlesinger in the CIA. Schlesinger, whom Carter has chosen to be his energy "czar," is a favorite of the harder-line interests.