The Senate Finance Committee spent most of yesterday morning discussing a problem that Chairman Russell B. Long (D-La.) said "challenges the statesmanship of any senator" --the so-called marriage penalty in the tax code.

That problem has "no political answer," Long declared, and he warned his fellow senators that, however they deal with it in the pending tax cut bill, "somebody is going to be sore at you."

The way Long proposed to deal with it, starting this spring or early summer most married couples filing joint returns would have their taxes reduced a little more than under the tax cut bill the House passed last week. Many single individuals, meanwhile would have their taxes reduced a little less.

In addition, an estimated 1.8 million single taxpayers would have a small increase in taxes present levels -- all average of $28 per person.

The committee may vote on the Long proposal today.

The marriage penalty arises from the standard deduction taken by the 70 per cent of all taxpayers who do not itemize their deductions.

Under present law the standard deduction is 16 per cent of adjusted gross income, which for most taxpayers is the same as total income; but the deduction is also subject to certain minimums and maximums. The minimums are $1,700 for single individuals and heads of household, and $2,100 for married couples filing joint returns. The maximums are $2,400 and $2,800.

The penalty occurs when two single taxpayers decide to marry. Suppose their incomes are such that they take the minimum deduction, as more than 50 per cent of all taxpayers do. Before marriage each taxpayer will be able to take a $1,700 deduction -- a total deduction of $3,400 from their two incomes. After marriage they will be able to deduct only $2,100. Their taxable incomes will be $1,300 higher, and their taxes will increase accordingly.

As part of its original plan to put more purchasing power in the economy, the Carter administration proposed increasing the standard deduction to a flat $2,400 for single taxpayers, $2,800 on joint returns. Then it realized this meant an increase in the marriage penalty in many cases.Two single taxpayers would have $4,800 in deductions before marriage and only $2,800 as a couple afterward, a $2,000 increase in taxable income. The administration thus amended its proposal to $2,200 for single individuals, $3,000 for joint returns, holding the marriage penalty to $1,400.

This second proposal, however, would have raised the taxes of some single individuals who now take the maximum $2,400 standard deduction, so the House made the new numbers $2,400 for single taxpayers and $3,000 on joint returns. But that put the bill back on the other horn of the dilemma, raising the marriage penalty to $1,800.

Long's split-the-difference proposal yesterday was $2,300 for single taxpayers and $3,100 for joint returns, which would make the marriage penalty $1, 500. The administration said it would have no objections; the total cost would not increase much.

Sen. Bob Packwood (R-Ore.) said he may also propose today that heads of household unmarried taxpayers with dependents -- be given the same deduction as couples filing jointly, instead of the same as single individuals. He said heads of household need extra help.

The tax code does not militate against marriage in all respects. As Sen. Daniel P. Mcynihan (D-N.Y.) pointed out yesterday, in one basic way it favors marriage; the rates on any given amount of income are lower for married couples filing jointly than for single taxpayers. But even here there is a complication. If one of the marriage partners earns all or most of the income, the couple comes out ahead. But if they each earn close to half, their taxes married will be higher than if they had stayed single.