A subtle shift has occurred in the long fight over the Equal Rights Amendment. Backers are desperately trying to make the amendment an establishment issue.

They are casting themselves as middle of the roaders. Militant feminists are being told to lower their voices and profiles. The tactical emphasis is on electioneering and hardball politics, not emotion.

ERA's most outspoken supporter here, for example, is Gov. Jim Hunt. Its chief lobbyist, Jesse Ray Scott, is the wife of another former governor. Its sponsor in the state Senate is Craig Lawing, a crusty but well-regarded conservative Democrat.

And when ERA supporters wanted to bring some outside guns into the state to promote their cause, they turned to two celebrities -- humorist Erma Bombeck and actor Alan Alda -- rather than to outspoken feminists. "You don't see the bra-burners out there in the forefront anymore," says one legislative oldtimer.

Still, ERA is in the North Carolina legislature, one of three states ERA supporters only a week ago thought had a reasonable chance of passing the controversial amendment this year.

"The proponents have become wiser in the ways of politics. They've become more sophisticated," says state Rep. George W. Miller Jr., an ERA supporter. "I think they're going to have to get even more sophisticated before we get this thing passed."

"The concern has been to bring forward moderate groups and show people that ERA is not a radical idea," he added.

In a Southern state like North Carolina, Which did not ratify the women's suffrage amendment until 1971 and didn't lift its ban on liquor by the drink until last fall, dispelling the idea that anything is radical is tricky business.

"The radicals, that's what has hurt this movement from the very beginning," says Lawing. "If we'd have someone like Bella Abzug or Gloria Steinem come down here this year, it would set us back 10 years. If those are the kind of people for it, a lot of people here are automatically against it."

To date, 35 of the 38 states needed to make it a part of the Constitution have ratified the ERA. The original seven-year period for ratification was to have ended March 22, but Congress last year extended the deadline until June 30, 1982.

Only one state -- Indiana -- has approved the amendment since 1977, but several have tried to rescind ratification. And national ERA supporters, fearing they have lost the momentum on the issue, were hoping that the amendment would be approved in North Carolina, Florida, Illinois and possibly Oklahoma this year.

It is not surprising that ERA backers are trying to picture the amendment as an establishment issue. After all, it is. It has been endorsed by the last three U.S. presidents, the Democratic and Republican parties, most labor unions, almost every major women's group in the country and a host of religious organizations.

The change in ERA tactics has occurred over several years. It became most obvious last fall when ERA measures appeared on the ballots in Florida and Nevada, and ERA groups targeted a number of legislators in Florida, North Carolina and Oklahoma for defeat.

The pro-ERA pitch in the two referendum states was largely an economic one. Television ads shown in Florida, for example, pictured a widowed older woman in a graveyard. "If we vote yes on [ERA], no state legislature ever, now or in the future, will be able to impose unfair and excessive inheritance taxes on our mothers, our wives or any other female member of our families," a voice said in the background.

A television ad in Nevada pictured a father with a daughter on a swing while a voice said: "By voting yes, you can be assured your daughter will never be deprived of a fair chance of an education, or if your wife has to work that she'll never be shortchanged on a paycheck because she's a woman."

The ads stress economic themes because "every time you ask someone what is good about ERA, the answer comes out, 'women will get equal pay,'" says Alice Kinkead, ERA director for the League of Women Voters, which commissioned the advertisements.

The ERA referendums lost in Nevada and Florida. But ERA backers scored several victories in legislative races, defeating state Sens. Ralph Posten in Dade County, Fla., and James McDuffie in Mecklenburg County, N.C., both of whom campaigned for ERA and then voted against it, and Mary Helm, a leading ERA opponent in Oklahoma City.

Since then, ERA backers have been looking for further victories. "We're attempting to avoid votes in places where it's not possible to win," says Sheila Greenwald, director of ERA-America. "We don't want a string of defeats."

However, legislators in Nevada and Virginia have rejected the amendment in recent weeks. And prospects dimmed noticeably in North Carolina last week, despite intense lobbying by Hunt and others.

"I would very much like to see North Carolina be the state to get this thing going. It would clearly indicate we're a state willing to go forward," Hunt said in an interview. "History is on the side of the proponents. It's simply something that is right and will prevail, either this year or later."

A hearing on the amendment is scheduled tomorrow, and a vote in the state Senate on Thursday. But last weekend ERA backers were three votes short and there were indications that they would attempt to keep the matter from coming up for a vote.

Meanwhile, fundamentalist church groups and other conservatives have mounted a vocal drive against the ERA. Undecided legislators report their mail running 3 to 1 against ERA, and some fear reelection defeat if they vote for the amendment.

"It pretty much boils down to a liberal-conservative fight," says a leading opponent. Rep. A Hartwell Campbell. "The liberals and city people are for it. The conservatives and rural people are against it.

"The forces that have been the leading proponents have created an image of women that is not popular here," he added. "I'd say women in North Carolina are more closely attuned to Anita Bryant than Gloria Steinem."