President Carter's proposal to register women for military duty could wind up costing the Equal Rights Amendment a victory Tuesday in the Virginia Senate where a former cosponsor of the controversial measure has now withdrawn his support.

"I don't want women in the draft of on the front lines -- it will probably hurt the military," said state Sen. Virgil H. Goode Jr. (D-Franklin County), a young attorney from rural Rocky Mount who has become the unlikely focus of a heated tug-of-war over the ERA issue.

The outcome is considered so close that one vote -- Goode's -- could decide it.

Goode, 33, voted for the constitutional amendment banning sex discrimination in 1977, the only other time in eight years that the measure has been debated and voted on in either house of the General Assembly. It was defeated then by one vote.

But then, Goode explained today, "the draft was not imminent. Now it is."

Concern about drafting women was raised last week when a Senate committee voted 9 to 6 to send the ratification measure to the Senate floor.

Because it is a constitutional amendment, the ERA proposal will need an absolute majority of 21 votes out of the Senate's 40 members. Without Goode's support, proponents and opponents alike say senators will come down to a 20-20 split on the floor.

Goode's announced defection from the ranks of ERA supporters has infuriated the amendment's backers and caused more than a few arguments at home with his pro-ERA wife, Martha. It has also thrown the issue into one of the most perplexing procedural tangles the assembly has ever experienced.

"It's a sticky, sticky situation," said Sen. Clive L. DuVal II (D-Fairfax), who has sponsored the amendment and will manage its fight through the Senate Tuesday.

It would be up to Lt. Gov. Charles S. Robb, an ERA supporter, to break a tie vote in the Senate.

ERA supporters and foes have been pouring over the state constitution and the Senate's rules for days -- with each side divided on whether Robb is legally entitled to break a tie vote on a constitutional measure. Robb has not said what he will do if the situation arises.

There has also been speculation that one or more opponents of the ERA will abstain or stay away from the Senate session altogether to avoid casting a tie vote that might bring Robb into the picture.

Some of the opponents have jokingly been calling each other "killer bees," a reference to Texas legislators who deliberately stayed away from floor sessions for days last year in an effort to torpedo certain legislation.There has been some talk in the Capitol of sending state troopers to fetch any Virginia lawmakers who try a similar tactic.

Goode, meanwhile, says he has been deluged with telephone calls and telegrams at home and at his Richmond office -- almost all urging him to support the ERA.

Barring "some revelation," however, he will vote against the amendment.

In addition to his opposition to registering women for the draft, Goode said he began to reexamine his support of the ERA after Congress granted what he considers an unfair time extension for getting it ratified. The amendment is three states short of the 38 states necessary.

He also acknowledges that the bulk of his constituents back home would probably vote against the amendment if given the chance, although a survey by ERA supporters of his district showed nearly a quarter of the residents polled were undecided on the issue.

Goode's wife said today that she has "expressed my feelings [for the ERA] as both a constituent and a wife" -- but to no avail.

"She is for it, and I'm against it," said Goode, who has changed his home telephone number to stem the tide of calls and dialed the telephone himself so that a reporter could speak to his wife.

"I'm a working woman and I have strong feelings about this; but I also realize that an overwhelming majority of his constituents are opposed," she said. The mother of an 8-month-old daughter, Goode said she teaches French language and literature at Ferrum College.

"I'm for the idea of equal rights, but I'm not a good arguer," she said, "Virgil can run circles around me." Still, she added that despite the awkwardness of their disagreement, her husband "is not the kind of person who tries to silence his wife."

The ERA debate is expected to last more than two hours. Its approval would send the measure to a House committee that has traditionally been hostile to the amendment.

Last weeks approval by a Senate committee, however, was the first time a Virginia legislative panel has ever approved the measure. Passage in even one house of a Southern stare, proponents say, would be "a shot in the arm" to ERA efforts around the country.