The House chamber looked like a matinee of "The Nutcracker" as the newly reelected Speaker Thomas P. (Tip) O'Neill Jr. announced that the first bill for the first session of the 98th Congress would be the one resubmitting the Equal Rights Amendment for ratification by the states.

The floor was awash in decked-out children, appropriately under fathers' care, and their reaction to the speaker's provocative declaration was what it had been throughout the proceedings: they squirmed, squealed, squawked, yawned, emitted piercing cries of "Daddy" or, in the case of one spirited toddler in a sailor dress, fled down the aisle on the Republican side. But the response of their elders to the news that ERA will be HR 1 was astonishing. Democratic daddies clapped and cheered. The Republicans hardly moved a muscle.

It was a remarkable show of something not immediately apparent. Was it a display of solidarity with the anti-ERA president? Did the Republicans want to serve notice on the speaker that, even in matters reflecting their own self-interest and even survival, they were not applauding any initiative from the Democratic side?

The Democrats, who have been hearing that Republicans got religion on women's issues during the recent campaign, were baffled and, of course, very pleased.

While the president is staying the course on the ERA, which was ratified by 35 states before the deadline passed on June 30 of last year, some people around him realize that the attitude of women toward Ronald Reagan, particularly in regard to the budget and nuclear arms, "has been translated into electoral behavior that is not good for Republicans." The quotation is from a leaked White House document on the Task Force on Women.

The newest memo to find its way to Capitol Hill--it is from Robert A. McConnell, who does legislative liaison work for the Justice Department, to Kenneth M. Duberstein, who does the same for the president--indicates further gnawing concern, at least in some quarters, that Democrats will capitalize on the sharp party differences on the question of women's rights.

"Indications are," McConnell wrote Duberstein, "that there will be significant activity . . . regarding multiple proposals perceived by their proponents to be pro-women."

By that he means the stated intention of Rep. Don Edwards (D-Calif.) to hold hearings on the ERA, which has 221 co-sponsors, among them 31 Republicans. Edwards is chairman of the subcommittee on civil and constitutional rights. McConnell is fearful that Edwards will attempt to "corner" the president on the ERA, just as he did on the Voting Rights Act--"thus forcing the president to support revolutionary legislation or to explain reservations to a public which perceives the president to be weak on women's issues."

McConnell cautions Duberstein against laying it all off on the Justice Department--"it has an extremely limited contribution to make."

"If," he writes a little desperately, "the administration has any hope of reversing the feminist momentum away from the administration, we must recognize that women's concerns are not generally so parochial as 'women this and women that' but arise from perceptions of the economy, military matters and other major national issues."

"Posturing," he says at one point, "will be critical."

But posturing will not be enough, says Judy Goldsmith, president of NOW, the National Organization for Women.

"Women are voting their independent interests, and are deeply involved in the political process. If Republicans don't understand this, they are going to go down with the ship."

Goldsmith points out that feminist candidates made exceptional gains in the legislatures of Florida and Illinois, two of the states that failed to ratify ERA.

Sen. Robert J. Dole (R-Kan.) has introduced a bill to remove all sex-bias language from the federal code, a proposal that he concedes to be "only a small step."

Democrats obviously have higher priorities than ERA. At least that is what they said during the campaign. It sounds more like politics, politics, politics than jobs, jobs, jobs, which they said was their most urgent task, followed closely by Social Security. But the fact is that they do not have a new version of the jobs bill that Reagan threatened to veto during the lame-duck session, and they are still far from having coherent legislation to reform and strengthen Social Security. ERA seemed like the perfect symbolic first.

And though the Republicans showed, in their coping with their young on the House floor, that they have made advances toward equality in child care-- several showed expertise in feeding, burping and rocking--they are not yet ready to show any real enthusiasm for equality between the sexes. The Democrats are delighted to accept complete custody of the issue.