Faced with a storm of citizen protest, the D.C. City Council is expected to try an extraordinary parliamentary maneuver today in an effort to reverse an estate tax bill it approved just two weeks ago.

Council member Polly Shackleton (D-Ward 3) announced that she will move to reconsider the bill proposed by Mayor Marion Barry and adopted by the council earlier this month. By late yesterday a majority of the council members indicated they were prepared to reconsider the measure.

There was some question, however, over the legality of Shackleton's proposal. Ordinarily reconsideration must occur before the bill is sent to the mayor for his signature into law.

The bill, enacted June 2 without any public hearings, repealed the city's inheritance tax, replacing it with an estate tax far higher than similar levies in Maryland and Virginia. "Ther really wasn't any public discussion of it. A lot of people didn't have any idea of the implications," said Shackleton.

Enactment of the tax bill triggered angry public protests and warnings that middle-income wage earners would flee the District to escape the extra taxation.

Shackleton said that if her motion to reconsider succeeds, she also will move -- and expects to be successful -- to table the legislation adopted June 2, allowing the council to start over on a new bill. An informal head count yesterday showed that 9 of the 13 council members were prepared to vote for reconsideration, including council member John Wilson (D-Ward 2) who introduced the bill. The only question is whether the reconsideration option is open to the council.

Since the council had completed action on the bill and sent it to the mayor, it is not longer in the council's hands. Council staff and attorneys were at work late yesterday afternoon trying to determine if there was a precedent under which the mayor may send a bill back to the council. If not, the option of reconsideration may not be available. If the mayor vetoes the legislation, the veto would automatically send the matter back to the council, but Barry is expected to continue his support for the bill.

Council Chairman Arrington Dixon said that if reconsideration is not possible, the council can use its emergency powers to repeal the bill in its entirety.

Rufus Lusk III, president of the Glover Park Citizens Association, said, "I think what people are afraid of is that the middle class is going to start leaving Washington." Lusk was one of a number of community activists who called council members or convened meetings to talk about the estate tax.

The charges exacted by the council simplify filing requirements and are expected to raise an estimated $4 million in new revenues, in fiscal 1983, the first year in which its full impact will be felt. But the changes also require taxes to be paid on life insurance policies with named beneficiaries, not previously considered part of a taxable estate. The revisions also mean that federal estate taxes no longer will be deducted from a person's taxable estate in the District.

The proposal was initiated by Barry and follows a recommendation four years ago by a prestigious commission that proposed several revisions in the city's taxes. A public hearing on a similar bill two years ago was canceled because of a lack of witnesses, Shackleton said.

The council adopted the bill by a 12-to-1 vote with only at-large member Betty Ann Kane dissenting. Kane was precluded from calling for reconsideration of the measure, since only a member who votes with the majority is allowed to ask for a rehearing.

"It [the vote] doesn't really say we did the right thing, but it's a very complicated issue," said Shackleton. "I think the proper work wasn't done on it, and the fact that there never was a public hearing negates what we did on it," she said. Shackleton said she has received approximately 50 calls protesting the act since news of its passage was published.

"I'm seriously considering moving to another state," said a Washington woman who said she had called Barry's office to protest the revised tax.

"It's shortsighted. I'm disgusted." said the woman, who asked that her name not be used. "I was going to buy a place in Florida to spend part of the time, but why not just simply sell and move?"