SINCE 1972 one of the nation's most respected public opinion research organizations has asked Americans what they think about legalized abortion. They have asked 12 times in 14 years and the results pretty much have seemed to remain constant:

About 4 people in every 10 approve of abortion on demand, about 1 in 10 opposes abortion under any circumstances, and about half those polled feel that abortion should be legal under extraordinary circumstances.

The surveys, done by the National Opinion Research Center of the University of Chicago, show that more than 8 in 10 people feel abortion should be legal if "there is a strong chance of serious defect in the baby" or "if a woman becomes pregnant as a result of rape," and 9 in 10 favor it "if the woman's health is seriously endangered."

By contrast, almost 6 in 10 say abortion should not be legal if a woman "is married and does not want any more children," and more than half are opposed in the instance of a single woman who finds herself pregnant but "does not want to marry the man." The public is evenly divided in the case of a family that is poor "and cannot afford any more children."

These attitudes have been so consistent in the Research Center's surveys and others over the past decade, varying by only a few points from year to year, that many opinion analysts tend to regard the public's views on abortion as locked in place.

However, this country has witnessed a massive easing of attitudes toward abortion in the past two decades, and there are signs the pendulum is swinging back.

There is only skimpy evidence about opinion on abortion before the 1970s, but what exists seems to confirm what many people believe intuitively, that attitudes grew sharply more liberal as part of the great social upheaval of the late 1960s.

George Gallup began taking the nation's pulse in 1935 but did not ask about abortion until 1962. That first inquiry came after an Arizona woman, Sherri Finkbine, went to Sweden for an abortion because she could not obtain one legally in the United States. She had taken the drug thalidomide and feared giving birth to a deformed baby.

A bare majority, 52 percent, said Finkbine had done the right thing, worlds apart from the 82 percent who have told the Research Center in recent years that they approve of abortion to avoid having a baby with serious defects.

The Center first asked its series of questions in 1965. It showed fewer than 20 percent approving abortion on demand, and more than 25 percent opposing abortion under all circumstances.

It was about that time that social change began in earnest. The nation's young people got to be more worldly than their elders, more educated, generally less concerned with religion. Many were sympathetic to the feminist movement. Each of these developments seems to have been pivotal in the shifting views on abortion.

For example, since 1972, the Research Center's polls have shown that an average 54 percent of the college graduates interviewed have favored legalized abortion on demand, compared with only 34 percent among people with less than a high school education. More college graduates in the 1960s and 1970s meant more tolerance for abortion. The same holds for religion. The surveys show 33 percent of Americans saying religion should have a less important role in American life, and 3 of every 5 such people feel a woman is entitled to an abortion for any reason. On the other side stand a slightly smaller 29 percent who feel religion should have a greater role. Among them, only 1 in 5 supports abortion on demand.

Similarly, the surveys show that men and women who support at least one aspect of feminism, the Equal Rights Amendment, are twice as likely to back abortion on demand as those who oppose ERA. Most Americans, especially the young and better-educated, do support ERA.

Perhaps the most striking change in attitudes has taken place among Catholics. In Gallup's 1962 survey only 33 percent of the Catholics interviewed supported Finkbine's decision. Yet the Research Center found that 77 percent of Catholics questioned since 1972 say abortion should be legal if there is a strong chance of a serious defect in the baby.

If attitudes changed in the 1960s, they became somewhat entrenched after the 1973 Supreme Court decision legalizing abortion, so much so as to provide strong evidence that government can decree morality.

Between 1972 and 1974, the Research Center's surveys showed increases of 6 percentage points in the numbers supporting the right of a single woman to have a legal abortion; 7 points for married women who do not want another child; 6 points for the very poor; 8 points in the case of rape or possible birth defects; 5 points for a woman whose health is endangered.

However, the assault on the Supreme Court decision by antiabortion groups in recent years, strongly supported by President Reagan, appears to be having some effect. Attitudes are heading back to the 1972 level.

The Research Center's figures for 1985, compared with those for 1980, show a 7-point decline in approval of legalized abortions for single women, an 8-point drop for poor women who can't afford another child, and a 7-point drop in the case of married women who don't want more children.