President Carter yesterday fought supporters of the controversial $2.2 billion plutonium breeder plant at Clinch River, Tenn., to a standstill in the Senate Energy Committee.

A proposal offered jointly by Sen. Frank Church (D-Idaho), who has led pro-breeder forces in the Senate, andcommittee Chairman Henry J. Jackson (D-Wash) to provide $75 million in continued funding to keep the project aline was defeated on 9-to-9 tie vote.

But an administration amendment offered by Sen. Howard M. Metzenbaum (D-Ohio) to spend $33 million to close down Clinch River lost 9 to 9.

The votes in a packed Senate hearing room marked a comeback for the administration from what some committee members and nuclear lobbyists on both sides of the question saw as a Carter defeat earlier in the week.

The House Science Committee has already voted to authorize $150 million for the Clinch River breeder reactor, which is designed to generate more nuclear fuel than it burns and was scheduled for completion in 1984. The Senate Appropriations Committee several days ago also voted in favor of $150 million in funding next fiscal year to continue the project.

The energy panel deadlock will almost surely lead to a Senate floor fight on the furture of the demonstration plutonium breeder, which has been plagued by recurrent controversy since it was first undertaken by the no wdefunct Atomic Energy Commission in 1969.

Church told committee members that he would offer his compromise $75 million amendment - the second compromise he as offered since proposing $120 million in funding Monday - to the full Senate.

Before the committee voted, Church left that hearing room to take a phone call from the President. "It was a cordial conversation; he restated his position," Church told a reporter after the hearings.

Senate Minority leader Howard H. Baker Jr. (R-Tenn.) is also expected to offer an amendment to provide $150 million for this home-state project when the committee bill comes to the floor.

The breeder is one of the projects covered by a big energy research and development authorization bill before the committee. After yesterday's votes, anti-breeder Sen. Dale Bumpers (D-Ark.) indicated he may try to keep the bill from being sent to the floor while he maneuvers to get his way on the breeder question.

But Jackson wants to move the legislation to the floor, and predicted that senators with home-state projects at stake will become impatient if it is delayed very long.

The White House did suffer one setback yesterday on Clinch River.

A General Accounting Office letter to Jackson and Baker said that President Carter "lacks legal authority to implement [this] plan" to use $31.8 million in congressionally approved funds to phase out work on the demonstration project.

Comptroller General Elmer B. Staats said, " to implement the President's plan without such authority would be in violation of the law."

The Clinch River breeder has been one of the most hotly contested energy battles in congress this year, and has become a symbol.

Carter opposes the use of plutonium, which would be the breeder's fuel, because it can be made into nuclear bombs and is extremely toxic. He wants to stay with uranium as a nuclear fuel.Uranium is used in the present generation of nuclear power plants. But breeder supporters say the United States could run out of uranium in the foreseeable future, and thus thatthe breeder is necessary.