In the summer of 1981 the White House political office took a poll in a Mississippi congressional district to see how the president's mixed position on extending the Voting Rights Act was playing in the South.

"When the results came back we were stunned," an administration official recalled. "We were looking for voting rights, and the big issue in the campaign to fill a House vacancy was Social Security. Something like 57 percent said they were voting against the Republican because of Social Security."

Dire political lore like that is the main reason for the curious impasse that exists over Social Security today. Almost everyone in America knows that Social Security is in trouble; its income no longer covers its expenses. Almost every elected official in Washington knows what is needed to solve the problem: some mix of tax increases and benefit cuts. But no one wants to be first to make the proposal for simple fear of retribution at the polls.

A White House official said, "Social Security has become a buzzword like busing and abortion were in the late 1960s and early 1970s. It's so hot there is no right side to take in that fight. I don't think we can educate people on the issue . . . . If we had the best solution in the world you know what would happen the minute we put it out, we'd get burned again."

Nor is this just the product of a bunker mentality in the White House. Abner J. Mikva is a judge on the U.S. Circuit Court of Appeals here. He was a Democratic congressman from Illinois, and a member of the House Ways and Means Committee, which has jurisdiction over Social Security.

"I don't know that this administration can depoliticize Social Security right now by claiming to want to do what is best for the country," he said. "There is too much of a perception of the administration as hostile to Social Security for them to propose ideas that would be viewed dispassionately. To get a bipartisan compromise you are asking the Democrats to forgo their political advantage on the issue and you are proposing to Republicans that they find a solution for which they'll get no credit.

"The best it could do for Republicans," Mikva said, "is to help them stop bleeding so profusely."

The Social Security issue has dogged President Reagan throughout his political career. It dogged the Republicans in the Nov. 2 midterm elections. In some polls about half the voters said one reason they favored Democrats was that they felt the Republicans were trying to cut Social Security benefits.

"I'm sure it was a factor," said former Republican representative John Rousselot of California, who was defeated in November. "From the exit polls we took the voters just said, 'Gee, maybe we'll take a chance on the Democrat because the Republican is going to cut Social Security benefits.' "

The Social Security situation briefly is this:

In May, 1981, his first year in office, President Reagan proposed deep cuts in Social Security benefits which he said were required to keep the giant trust funds solvent. Democrats quickly attacked him on grounds he had proposed much more than was needed, and was really trying to balance the budget on the backs of the elderly. Reagan finally withdrew his proposals when even Republicans deserted him, and instead named a bipartisan commission to study the problem and recommend solutions.

The commission's report is due next week, and the Ways and Means Committee is scheduled to start hearings next month. The largest of the Social Security trust funds will run out of money on July 1 if Congress takes no action in the interim.

But the commission is deadlocked more or less along party lines, with Democrats leaning more toward tax increases to shore up the system and Republicans more toward benefit cuts. Commission leaders have urged Reagan to step in and help them resolve their differences. He has refused.

"Social Security was made a political football and not by us and not by me," Reagan said at his news conference this week. "I believe that for me to now impose myself . . . and say 'Hey, fellows, this is the way I want you to go,' . . . I would then cock my ear and wait for the loud outcry from Capitol Hill and the same old political football would be seen going up in the air like a punt on third down."

But some students of the issue think that this hands-off posture may be a mistake, and not just for substantive but for political reasons.

"They the president and his aides may have made a mistake by not seeing that there was never a chance for the commission to come together on a plan unless the White House gave them the green light," said Bert Seidman, the director of Social Security at the AFL-CIO. "The president had to have some political exposure even if it was in private with the commission. Avoiding the issue altogether invites more political problems."

Rep. Barber B. Conable (N.Y.), ranking Republican on Ways and Means and a member of the presidential commission added, "I told the president he should at least contact Tip House Speaker Thomas P. (Tip) O'Neill Jr. . The way things are going Tip could propose a big tax increase to fund the system and then the president would have to veto it. Then Tip could say to people that the checks didn't go out because the president vetoed the money."

But the White House, whose strategist on the issue has been chief of staff James A. Baker III, is not budging.

Baker has held talks with commission members, but these have been carefully guarded, so as not to expose the president. Nor is it clear that the president will make proposals even after the commission reports.

"We're not going to get a report and adopt their proposals or offer our own," said one White House source. "What we can do instead is wait on Tip. He has the super-majority in the House now, so he can't say the president isn't doing anything about Social Security. He can do something with Social Security if he wants to and then we'll see what we think."

Senate Finance Committee Chairman Robert J. Dole (R-Kan.), also a commission member, said at one point that the White House was "frightened" of Social Security.

He later went to Baker to smooth things out, but "I was accurate when I said they are frightened of Social Security," Dole said. "I don't mean to suggest that the president himself was frightened, but certainly the people advising him. They don't want to raise Social Security as an issue at all. They didn't want to raise it before the election for fear they would get clobbered. In my view they should have addressed it early on and we would have had it behind us."

Dole said that if the president had the commission produce a list of options and gave them to the Congress to choose from then political fallout to the president would be limited because "he wouldn't have any fingerprints on it."

That fingerprints issue is important to the president. According to poll data, Reagan tends to be seen by the public as an enemy of the program. This is especially true among the elderly, who in 1980 were among Reagan's biggest supporters.

But in 1982, an ABC News opinion survey of voters leaving polling places showed a nearly 2-to-1 disapproval rate (64 to 36 percent) for Reagan's handling of Social Security. And of those 64 percent who disapproved of his handling of the issue, 72 percent of them voted for Democratic candidates.

In a September CBS-New York Times poll Social Security was cited more often as a decisive issue by voters (61 percent) than Reagan's economic program (56 percent); defense spending (55 percent) or the balanced budget amendment (47 percent).

In another national poll done after the midterm election by William R. Hamilton & Staff of Chevy Chase, 52 percent of the respondents said Democrats would do a better job than Republicans at handling Social Security. Only 17 percent said Republicans would do a better job with the balance undecided or having no opinion.

Fifty-two to 17 is close to 3 to 1. No politician wants to be on the wrong side of odds like that.