The Senate yesterday opened debate on a constitutional amendment that would permit legislation banning abortions, but the prime sponsor conceded that chances of passage are dim, and a leading opponent claimed that the anti-abortion drive is "over the hill and close to finished."

The 10-word amendment, proposed by Sens. Orrin G. Hatch (R-Utah) and Thomas F. Eagleton (D-Mo.), would overturn Supreme Court decisions upholding the right to abortion and would empower both Congress and state legislatures to ban or restrict the procedure.

The amendment states simply, "A right to abortion is not secured by this Constitution."

A two-thirds vote of both houses is required to approve the amendment and send it to the states for ratification, and Hatch conceded even before the debate opened that the votes probably "just aren't there" to pass it now.

But he said it was important as a first step and as a "benchmark" against which to judge senators on the abortion issue. "This is the most important vote on abortion ever held," said Hatch.

A vote on the amendment is scheduled for late today.

Sen. Bob Packwood (R-Ore.), leading the floor fight against the amendment, disputed Hatch's contention that the right-to-life movement is gaining strength, and claimed he had a minimum of 42 votes, more than enough to block passage.

But he conceded that this would be barely enough to sustain a filibuster, which could take as many as 41 votes. Sen. Jesse Helms (R-N.C.) has served notice that he will attempt to put anti-abortion riders on regular legislation as the year goes on.

Hatch said President Reagan is expected to make telephone calls on behalf of the amendment to some of the 10 senators who he said are wavering on the issue. But Packwood said the calls wouldn't do the amendment any good.

"He will not turn a vote on it. This is not AWACs," he said in a reference to the Saudi Arabia sophisticated aircraft and equipment sale that Reagan influenced. "People know where they are" on abortion.

The debate opened on a relatively calm note, compared with the impassioned oratory that has arisen over the issue in the 10 years since the Supreme Court upheld the right to abortion. But big charts displayed in the back of the chamber cast a shadow of the furies that the issue has unleashed.

One showed "American War Casualties," which Hatch said showed that abortions "cost 10 times the human life of all our wars put together." Another chart showed poll results on when people think life begins, with men's responses shown in blue and women's in pink.

Hatch contended that the Supreme Court has enunciated a policy of "abortion on demand," which he said is "more radical than any other nation with the possible exception of the People's Republic of China."

Disputing Hatch's "abortion on demand" conclusion, Packwood said a "basic civil right" was involved that is "too precious to be decided by a majority vote" of Congress or state legislatures.

Sen. Mark O. Hatfield (R-Ore.) supported the proposed amendment as a defense against "dehumanization of life," which he said also results in "oppression against minority groups, exploitation and misuse of our natural resources and reckless, destructive foreign policy." Abortion, he said, is "the destruction of life . . . . It cheapens life."