While President Reagan and his aides were congratulating themselves publicly last week on surviving the lame-duck session of the Congress, the behind-the-scenes talk in the White House about Social Security did not reflect the cheerful mood of the holiday season.

Reagan is, as always, an incorrigible optimist. But top-ranking members of the president's many-voiced White House staff recognize that the Social Security crisis is coming at them with locomotive speed. The administration is tied to the tracks, with no rescuer in sight.

The president did buy himself two weeks by extending the life of his advisory commission on Social Security, now due to report in mid-January. But the report is unlikely to solve Reagan's political problems.

Reagan reportedly opposes the acceleration of Social Security tax collections from workers, recognizing that this will reduce purchasing power and delay his long-promised economic recovery. But if he supports cutting future cost-of-living increases for recipients, he knows that he will be portrayed as having broken a campaign promise to preserve the system's benefit levels.

"It's a classic no-win political situation," acknowledges one aide. "Heads we lose. Tails, the Democrats win."

The administration's predicament is compounded by public opinion surveys showing that a large majority of Americans, confronted with the choice of raising taxes to pay for Social Security or slowing the rate of benefit increases, don't want to do either.

And neither does the White House staff, which badly burned the president by putting him out front in 1981 with a "reform" plan that was subsequently repudiated by Republican members of Congress. This time, White House chief of staff James A. Baker III doesn't want the president cast in the lead role.

In fairness to Reagan, he has been saying for nearly 20 years that the Social Security system would face this crisis. His own deeply held view is that fundamental changes must be made, preferably in capping cost-of-living increases, which have risen more than either wages or productivity. Whether he accepts the political risk of disregarding his own staff and saying so directly, in the face of accusations that he wants to do in the system, may provide an early clue as to whether he is, in fact, seeking reelection in 1984.

What is known now is that those same White House aides who are predicting that Reagan will run again are also the ones who want him to stay away from Social Security. Their hope is that, if Reagan does nothing, the Democrats will be forced to make the first move.

It is an approach that courts disaster and is made to order for opponents who will portray Reagan as abdicating leadership while still secretly seeking Social Security cutbacks. But this wait-and-see approach is what now passes for strategic political thinking in the high councils of the White House.

In his calls for businesses to hire extra workers and his statements in interviews that economic recovery is the solution to the problems of the federal budget, Reagan is signaling his administration's early themes for 1983.

Some of these ideas are likely to show up in the State of the Union message, which is still in the talking stage.

Nothing is written yet, say senior administration officials, one of whom recalled the amusement at the White House last year when the planning and evaluation shop headed by Richard Beal produced a 32-page memo for the speech and a summary of helpful hints. The speech, Beal recommended, should be (1) oral, (2) televised, and (3) written by a good speechwriter.

Nothing was said about praising motherhood or apple pie.

Reagan heads westward today, for a week that will be spent mostly in Palm Springs, Calif., where he will celebrate New Year's Day in comfortable surroundings.

Before Palm Springs, the president will recommisssion the battleship New Jersey, a showcase of modern naval technology, in Long Beach harbor.

Making the case for battleships, Secretary of the Navy John F. Lehman told reporters in the White House last week: "You've seen Henry Kissinger stand here in this building in times of crisis and say the first question the president asks in times of crisis is 'Where are the carriers?' " Now the first question will be 'Where are the carriers and the battleships?' "

Inadvertently, in discussing Reagan's foreign travel plans last week, I said he was looking forward to a "small country" trip -- with Ireland, Sweden and Austria the possibilities -- in 1984. It should have been the fall of 1983.

After 15 minutes with reporters in the White House briefing room last Thursday, Reagan was apologetic when an aide, by pre-arrangement, cut off the questioning.

"Listen," the president said. " . . . I know there are a lot more hands and I'll try and see you more often. But I am now 31 minutes late for lunch with the vice president and you know how irritated George can get . . . ."

The last time some of us saw Vice President Bush irritated was when Reagan creamed him in the 1980 debate in Nashua, N.H.

Reagan, incidentally, is pleased with the results of his new openness, which included four interviews and two "press availabilities" this month. He has promised to do more of the same next year.