The Carter administration voiced "major objections" yesterday to the tax bill drafted by the Senate Finance Committee, complaining that it would cost the government too much and is "unbalanced" in favor of high-income investors.

In a letter to all the senators, Treasury Secretary W. Michael Blumenthal warned that the bill would drain so much revenue in coming years it would "prejudice our efforts to reduce the budget deficit."

He also asked senators to vote to reduce the bill's $3.1 billion in capital gains tax cuts, which would primarily benefit high-income investors, and to redistribute the breaks among middle-income taxpayers.

"I'm sure you agree that every taxpayer should contribute a reasonable amount to the costs of government," Blumenthal wrote. "The Senate Finance Committee bill does not accomplish this objective."

Blumenthal's letter-writing campaign marked the opening of what officials say wil be an all-out effort by the administration to amend the tax bill on the floor. The Senate is scheduled to take it up tomorrow.

The secretary's note was accompanied by a 55-page analysis outlining the administration's position on each provision in the bill. In virtually every instance, Carter's stand was known before.

The Finance Committee has recommended some $23 billion in tax reductions for this year and next, combining a $16.3 billion tax bill approved by the House with extra reductions for both high-and low-income brackets.

It also has voted to weaken the present "minimum tax" on high-income investirs in a way that Blumenthal contends will enable wealthy persons to use tax shelters more effectively to escape payment of taxes.

And if has tacked on dozens of special-interest provisions containing tax breaks for specific industries or companies - from a $7 million break for two airlines to a new investment tax credit for pig-pen owners.

Senate liberals have served notice of plans to try to amend the bill this week to meet some of the administrations objections, but it's uncertain how they will fare.

Blumenthal told senators yesterday the Finance Committee bill would exceed the cost of President Carter's original tax cut proposals by $5.4 billion in 1979, rising to $6.7 billion in fiscal 1981 - a margin he called "excessive."

Unless the cost of the Treasury is trimmed, he warned, the bill "would seriously compromise" the administration's ability to control inflation by reducing the budget deficit, as Carter is hoping.

He also urged senators to reduce the capital gains tax cuts and to strengthen the Finance Committee provision affecting the minimum tax. And he opposed after writeoffs for business.

Carter already has threatened to veto the House version of the legislation. Treasury strategists are hoping to influence the forthcoming House-Senate conference but say a veto still is a possibility.