By setting peak goals for halting the arms race, President Carter has raised a formidable challenge for his own administration to match words with action.

The President caught his own embryonic administration by surprise yesterday as dozens of questions immediately leaped out of his interview remarks on U.S.-Soviet nuclear policy. A week ago, similar generalities by the President-elect could be answered with generalities; but not this week.

Secretary of State Cyrus R. Vance, officially entering the State Department for the first time yesterday with that title, faced the first barrage of reporters' questions.

Vance said, in essence, that the Carter administration needs time to "complete our homework on this" before opening up discussions with the Soviet Union, "probably . . . around the end of March."

There are subjects on the U.S.-Soviet agenda, however, that may require much earlier decisions, at least decisions to postpone action.

Two interlocking treaties are now pending before the Senate, signed but not ratified. One is treaty, signed in Moscow in July, 1974, to ban underground American and Soviet nuclear weapons tests larger than 150 kilotons. Accompanying it is a company treaty to limit to the same level underground blasts of nuclear explosives for peaceful purposes, signed on May 28, 1976.

Both treaties are controversial, criticized on grounds that they are ineffectual. President Carter has now reiterated his campaign commitment to eliminate "the testing of all nuclear devices, instantly and completely."

On its face, that may appear to parallel a Soviet position, that "nuclear weapons testing should be stopped everywhere, and by all."

But in fact, the pending treaty to permit continued "peaceful" nuclear explosions was laboriously negotiated to fit Soviet insistence. The Soviet Union is continuing a program that the United States abandoned, to use nuclear blasts to alter the courses of rivers, throw up earthen dams, dig craters.

Broader differences run through many of the views expressed by Carter and Soviet leaders, even though the declared goals appear similar.

President Carter has reiterated his desire "to move very quickly" to a reduction in nuclear weapons, "even prior" to a new strategic arms limitation talks (SALT) accord.

Carter suggested that "there would be a two-stage evolution," completing the new SALT II agreement and simultaneously barganing with Soviet Union over "reductions on atomic weapons."

Soviet leader Leonid I. Brezhnev, however, said on Jan. 18 in the Soviet city of Tula, that:

"The Soviet Union, naturally, is prepared to advance further in questions of limiting strategic armaments. But at first it is necessary to consolidate what has already been achieved and to implement the [SALT] accord reached in Vladivostok," because the temporary U.S.-Soviet limit on offensive nuclear weapons expires in October.

To add "new questions to those that are being currently discussed," Brezhnev said, "will only further complicate and procrastinate the solution of the task in general."

Similarly, President Carter, like the Soviet leadership, has stated that his ultimate objective is to eliminate all nuclear weapons.

But in order to move toward that goal of what the Russians call "general and complete disarmament," the Soviet position is that all nations with nuclear might, especially China - the Soviet Union's arch ideological rival - must be equally committed to disarm.

Carter, however, has suggested a different approach: starting with a U.S.-Soviet accord "for major reductions on atomic weapons," with "the next step" to be attempts to win agreement by China, France, Britain and other "atomic nations" to join the disarmament pact.

Secretary of State Vance, encountering a rush of questions over the Carter interview, as he entered the State Department, was asked if President Carter was saying the United States will take "unilateral action," if necessary, to halt all nuclear testing.

Vance, apparently caught off guard, said, "I do not know. "We have not had a chance - he and I - to discuss that point."

Later in the day a spokesman said that the answer was "unequivocally no, we are not advocating unilateral halting to the testing."

Another point clarified later in the day was whether there was a conflict between President Carter's reference to receiving "an encouraging message" from the Soviet Union, and Vance's denial that any new message was received.

A spokesman said afterward that there was "no conflict." Carter, the spokesman said, was referring to earlier statements by Soviet leaders that indicated "high level interest" in reaching new accords.

Questions also were raised about whether the President was declaring a major change in the U.S. position on the two longstanding obstacles to a SALT II accord. There are disagreements on counting the Soviet bomber known as Backfire, and American-developed long-range cruise missiles.

President Carter said, "I would not let those two items stand in the way of some agreement," while Vance said: "The questions of cruise and of Backfire are still very much open for discussion . . . with the Soviets with respect to SALT II."

A State Department spokesman said, "There is no conflict between the two statements." Carter, the spokesman said, was not dismissing the two obstacles, but instead was saying that these two subjects "would not be the issues that would sink the SALT talks." The President, it was said, "was asserting his determination to find appropriate and military acceptable solutions" to the disputed weapons systems.