The Senate Finance Committee last night approved a $23 billion tax cut bill the Carter administration says would bust the federal budget and is tilted too far in favor of the rich.

The legislation was sent to the Senate floor by a vote of 15 to 2 despite a threat -- carried to the senators by Treasury Secretary W. Michael Bluemuthal yesterday morning -- that the president will veto it if it is not amended.

The committee tried to meet some of the president's objections yesterday afternoon by adjusting the rate cuts in the bill to give extra relief to low and middle-income taxpayers.

It also voted to scale back a House-passed provision exempting from taxation the first $100,000 in profits on the sale of a home.

But the senators left intact the main source of Carter's opposition, a tax cut of about $3 billion voted earlier by the committee on capital gains, the profits from sales of stocks or other assets. Three-fourths of this savings would go to taxpayers with incomes over $50,000.

In the final hours of action on the bill the committee, as is its custom, also added a number of "minor" amendments, pet proposals of one senator or another.

Last night's collection included one special tax cut for horse breeders, another for the proprietors of sod farms and a third for chicken farmers in Maine and Arkansas. The senators also tacked on a special $7 million tax cut for Texas International Airlines.

All four of these were proposed by the ranking Republican on the committee. Cart Curtis of Nebraska, who is retiring this year.

The committee bill would give a family of four with a $15,000 income a $97 tax cut next year. For the same size family with a $30,000 income, the savings would be 356. Both cuts are larger than they would be under the $16.3 billion tax cut bill passed by the House.

Committee technicians, said last night the tax cuts for individuals in the bill would be enough to offset next January's scheduled increases in Social Security taxes, plus one year's inflation, but no more.

The bill is expected to go to the Senate floor next week.

In addition to other possible problems, the committee bill plus other tax cuts in the legislative pipeline would go more than $1 billion beyond the limit allowed by the congressional budget resolution for next fiscal year, a breach that could draw opposition from some fiscal hard-liners when the bill comes up for a vote.

Sen. Russell B. Long (D-La), chairman of the panel, said Congress may end up having to trim some of the other pending tax measures, such as the tution tax credit bill, to make up the difference. Long virtually invited Carter to veto the tuition credit bill.

The tax bill approved yesterday contains $15.9 billion in cuts for individuals - including an increase to $1,000 in the $750 personal exemption allowed each taxpayer and dependent - and $4.5 billion in business tax cuts, both from reducing corporate tax rates and bolstering tax incentives for hiring and investment. In addition to these amounts, there would be a net cut between $2.5 billion and $3 billion on capital gains.

The bill would triple the House-passed reduction in capital gains taxes by exempting 70 percent of a gain from taxation instead of 50 percent, as now. It also would defer a key 1976 tax "reform" increasing income taxes on sales of inherited property.

The bulk of the tax reduction in the bill, including those for wage-earners, would become effective Jan. 1. However, in an attempt to pep up the stock market, the panel voted to make the cut in capital gains taxes effective Nov. 1.

Despite Blumenthal's veto threat, the committee's action yesterday does not guarantee the president will reject the tax bill. Administration officials expressed hope the bill could be changed further when it goes to a House-Senate conference committee.

In addition to the extra rate cuts voted for low and middle-income households, the committee earlier approved $1.8 billion more than the House in tax breaks for low-income persons by liberalizing the "earned income" credit for the working poor. Those too poor to qualify for a tax break would be skewed primarily toward taxpayers in the $10,000 to $40,000 income brackets, the group most slighted by the House bill. For a family of four earning $12.500 a year, the tax cut would total $125, compared with $105 in the House bill.

In addition to its other actions yesterday, the committee also:

Made permanent the 10 per cent investment tax credit for business, and liberalized it so corporations could use it to erase 90 percent of their tax liability, rather than 50 percent as now.

Approved a new proposal to provide holders of municipal bonds with a choice of accepting their interest tax free, as now, or including it in their adjusted gross income and claiming a credit to offset any tax. Besides benefiting taxpayers, in the 40 percent bracket and below, this would be a first step toward enabling middle-income taxpayers to take advantage of the favored tax status of municipal bonds.

Approved a proposal to increase the standard deduction or so-called a "zero bracket amounts" for single heads of households from 2,300 to $3,000, raising the income floor below which such persons would not have to pay any taxes.

Agreed to allow totally disabled taxpayers an extra personal exemption such as now is available to blind persons, provided the disabled persons do not receive other federal welfare or veterans benefits. The additional exemption would amount to $500 next year, rising to $1,000 in 1981.

Yesterday's measure would reduce taxes for an estimated 65 million taxpayers - mostly in the $10,000 to $100,000 brackets - with specially large cuts for families with two or more children. It also would provide extra cash payments for 3 million working poor who earn less than $5,000 a year.

At the same time, about one million persons - most of them single taxpayers who itemize their deductions - would suffer a tax increase if the measure is passed. The bill also would raise taxes for some 32,000 high-income investors who would have to pay a new "alternative" minimum tax.

Yesterday's changes involving the homeowners provision effectively would scrap the proposal passed by the House to allow those selling a home a once-a-lifetime opportunity to take the first $100,000 from their profits tax free even if they don't spend it on a new, more costly home.

The Finance Committee version, which would be retroactive to sales after July 26 of this year, essentially would liberalize a provision in current law that allows homeowners aged 65 and over to exclude $35,000 or more from the sale price of their homes in computing the amount of their profits subject to tax. The calculation involves a complex formula.