The new Republican majority on the Senate Judiciary Committee flexed its muscle yesterday, and out popped a proposed constitutional amendment designed to produce balanced federal budgets.

It was the first time such an amendment has been sent by committee to the Senate floor, and now that conservatives have taken control, it may be only the first of several dealing with such highly controversial subjects as abortion, the death penalty, school busing and prayer in public schools. On the House side all such amendments are still bottled up by liberals in the Judiciary Committee.

In the last Congress, the balanced-budged amendment was killed in the Senate committee by a one-vote margin. This year, like last, Sen. Charles McC. Mathias Jr. (R-Md.) was the only Republican to vote against it. But two Democrats joined nine other Republicans to make the vote 11 to 1. Six absent Democratic liberals were given permission to vote late, but if all voted no the proposal would still be approved 11 to 7.

The proposed amendment provides that beginning the second year after it is ratified Congress must approve balanced budgets for the federal government unless three-fifths of the members of both houses vote to permit deficits. The requirement could be waived by simple majorities in time of war declared by Congress. Once the balanced budget was approved, Congress would be forbidden to pass or the president to sign any budget-busting legislation.

The proposed amendment also provides that federal receipts could not increase at a rate faster than national income unless Congress so provides by majority vote.

A constitutional amendment that starts in Congress must be approved by two-thirds of both houses and by legislatures of three-fourths of the states to become part of the Constitution.