Senate Majority Leader Robert C. Byrd (D-W. Va.) yesterday formally announced that there will be no SALT debate this year, a symbolic admission that could be a prognosis for next year as well.

The treaty now passes into the season of presidential politics. Whether the Senate will be willing to deal with it under those conditions remains to be seen.

Some of SALT's ardent supporters insist that the treaty still has reasonable prospects in the Senate, but others have become disheartened. Even the optimists say that President Carter will need an extraordinary run of good luck and good political management to salvage the treaty.

Since the Senate recess in August, the treaty's prospects have dimmed appreciably. The pool of undecided senators from which a two-thirds majority of 67 would have to be built has shrunk substantially as a growing number of senators have indicated their opposition to SALT II.

A careful count of the Senate at this time suggests that there are 53 to 55 votes for the treaty, 27 to 30 against and 15 to 20 undecided.

Byrd, a careful head counter, has to realize that finding enough senators to create the necessary majority of 67 will be extremely difficult. Even SALT supporters say it would be impossible to do now.

In recent weeks, several senators optimistically counted by the White House as possible SALT supporters have drifted into apparent opposition. Among them were Dennis DeConcini (D-Ariz.), Richard Stone (D-Fla.), William S. Cohen (R-Maine) and John W. Warner (R-Va.).

But SALT's future could be further endangered by an ambiguous or politically damaging outcome in the crisis in Iran. The current mood of uncertainty about America's role in the world -- notwithstanding the Tehran crisis -- has already been working to SALT's disadvantage in the Senate.

Almost any outcome in Iran could lead to a national reassessment of America's position in the world, and many senators could take the position that SALT should be set aside during such a reassessment.

The most determined opponents of SALT II in the Senate have long regarded delay as their ally. Some of them have been predicting that the Senate vote on the treaty will simply be delayed indefinitely, a prospect that now seems more real, even to treaty supporters.

"The pressures are going to be awfully strong to go over into 1981," one conservative Republican predicted yesterday. Last August, the same senator predicted that SALT II would win Senate approval this year.

That prediction was made at the end of initial hearings on the treaty in the Armed Services and Foreign Relations committees, when it appeared to many in the Senate that momentum was building behind the treaty. The flap over Soviet troops in Cuba a few weeks later undid that momentum, and pro-SALT forces have never really recovered.

According to senior White House officials, Carter is aware of the unfavorable alignment of forces in the Senate now, but wants to press ahead with the treaty debate on the grounds that SALT II is more necessary now than ever.

For example, one official said, the events in Iran emphasize the potential perils of a Pakistani nuclear weapons or other proliferation of nuclear capability into generally less stable Third World countries. Without approval of SALT II, this official argued, the effort to control proliferation could be gravely weakened.

The Iranian crisis is likely to exacerbate tensions and intensify competition between the Soviet Union and the United States in the so-called "crescent of crisis" in the Middle East and Asia, the same official argued, and this competition would be much safer and sanner in a world that included SALT II.

But several Senate sources speculated that, in a crunch, Carter would have to conclude that no vote on SALT would be better for his reelection campaign than an outright rejection of, or fundamental amendment to, the treaty.

If SALT can be revived next year -- and even its ardent opponents don't rule out this possibility -- there are several possible developments that could work to its advantage. The key among them would appear to be a happy ending in Iran.

The administration's efforts to reshape its defense budget to please senators concerned about the nation's military posture could also prove helpful to SALT. The White House has moved far from its initial inclinations to increase proposed defense spending by many billions of dollars in hopes of winning more votes for the treaty.

The apparently declining fortunes of Sen. Howard H. Baker Jr.'s (R-Tenn.) presidential campaign might increase the chances of getting some more Republican votes for SALT, one Senate source speculated. This theory was that if Baker does not appear to be a frontrunner for the nomination, other Republican senators loyal to him will be less reluctant to defy his leadership and vote for SALT II, which Baker opposes.