With two votes to spare, the Senate yesterday approved and sent to the House the balanced-budget amendment to the Constitution.

The vote was 69 to 31 for the controversial proposal, which would require three-fifths of both houses rather than the present majority to unbalance budgets in the future. The votes of 67 senators--two thirds of the Senate--were required for the amendment to pass.

The Senate vote was the high point so far in a protracted national debate, born in part of public dissatisfaction with soaring deficits and nourished by politicians' fears that they would reap the whirlwind in an election year in which they passed a federal budget that will wind up much more than $100 billion in the red.

In the Republican Senate, this fear proved decisive. But the next step, in the House, is more uncertain. A similar measure there is bottled up in committee, opposed by the Democratic leadership, and faces a parliamentary thicket if it ever reaches the floor.

A major complication in the House will be an addition to the amendment, approved Tuesday by the Senate, requiring a three-fifths vote of both houses not just to unbalance budgets but to raise future federal debt ceilings.

The House version does not have this extra provision--and House supporters have been trying to move it out of the hostile Judiciary Committee and onto the floor through a discharge petition which would prohibit floor amendments.

The House could thus not pass the same language as the Senate and the amendment would have to go to a House-Senate conference where the controlling House conferees would be Democrats intent on killing it.

If finally approved by both houses, the amendment must be ratified by 38 states. So far, 31 state legislatures have approved resolutions of some sort calling for a constitutional convention to draft a balanced-budget amendment.

As the roll call unfolded tensely at noon, all but seven Republicans voted for the measure, which would be the 27th amendment to the Constitution. The Senate Democrats, who had never established a position on it, split down the middle with 22 of the 46 voting for it.

The outcome was in doubt until the last few senators wandered into the chamber, producing the final cluster of votes that put it over the top. Sen. Robert C. Byrd (D-W.Va), the minority leader, withheld his decision until the final moments and then voted for the measure after the outcome was settled.

As expected, the outcome hinged on a half-dozen senators. One, Sen. John Heinz (R-Pa.), switched positons to oppose the amendment, but other previously uncommitted members voted for it.

"It's fair to say we were sweating bullets all the way," said an aide to the majority leader, Sen. Howard H. Baker Jr. (R-Tenn.). Until the end, Baker was unsure of at least three votes--Sens. Arlen Specter (R-Pa.), Russell B. Long (D-La.), and Alan J. Dixon (D-Ill.)--who all voted for the amendment. Two who had expressed misgivings--Sens. Jeremiah Denton (R-Ala.) and Howell Heflin (D-Ala.)--also voted for it.

President Reagan had endorsed the amendment, but the strongest grass-roots pressure in its behalf came from movements stirred up by two organizations, the National Taxpayers Union and the National Tax Limitation Committee, which have spent years generating support for both a balanced-budget amendment and a ceiling on federal spending.

Opponents dominated the last minutes of debate, arguing that the amendment was either an unworkable gimmick to fool voters or a constitutional straitjacket that would implant a particular economic theory in the Constitution.

Sen. Nancy Landon Kassebaum (R-Kan.) accused the Senate of being "hypocritical." She said, "It's easier for us to vote for a constitutional amendment than to balance the budget."

Others contended that many supporters actually disowned the amendment privately while voting for it publicly to pacify constituents.

"If this were a secret ballot, it wouldn't get 15 votes," Sen. Patrick J. Leahy (D-Vt.) contended.

Baker appealed for support without extolling the amendment's features, arguing merely that the states are due an opportunity to vote it up or down.

Sen. Alan Cranston (D-Calif.), who led opposition forces, predicted after the vote that the amendment will not pass through Congress this year and will never be ratified by the necessary states.

The amendment would prevent Congress from passing a budget in which outlays exceed receipts unless the country is at war or unless both houses, by three-fifths majorities, vote to approve a deficit.

The House version is now penned in the Judiciary Committee, whose chairman, Rep. Peter W. Rodino Jr. (D-N.J.), is strongly opposed although he may produce an alternative measure which would be substantially different from the Senate version but would allow members to vote on some kind of budget-balancing procedure.

Reagan yesterday hailed the Senate vote as a victory in which members of both parties combined to "resist intense special interest pressure for still more red-ink spending." He called on House Democratic leaders to "heed the will of the people" and permit a vote on the amendment in that chamber.