There's a full-fledged row going these days about Uncle Sam's big best marital problem - the so-called "marriage penalty" imposed on couples by the nation's tax system.

Because of quirks in the tax structure, a man and a women who both work now pay more in taxes if they marry than they would if they stayed single.

For most couple, the extra tax tab is modest - say, from $30 to $150 a year. Forthose in the $50,000-a-year income bracket, it can run as high as $1,188.

With a greater proportion of the nation's married women working these days, the problem has grown into a political brouhaha - with more and more young couple protesting the disparity as unfair.

It's especially uncomfortable for President Carter. Throughout his campaign and first few months in the White House, Carter made a point of frowning on couples who live in "sin."

Now that he's in office, the President hardly can appear to ignore a tax situation that critics say tends to discourage marriage. Yet, under present law, a man and woman technically are "better off" - from a tax standpoint - living together than tying the knot.

The problem is, tax experts can see no sure way of eliminating the "marriage penalty" altogether without creating other, more serious inequities in the tax system. Carter already has scrapped one plan for reducing the over-taxation of married couples, and may have to compromise on another.

The difficulty stems from the basic makeup of the tax structure - specifically, that the tax system tries to adhere to several broadly conflicting principles at once:

On one hand, American tradition dictates that the tax system be "progressive" - that is, that higher-income taxpayers pay proportionally more in taxes than those at the lower end of the income scale.

For example, a person earning $30,000 a year should, by rights, have to pay substantially more in taxes than either two others earning $15,000 each.

At the same time, however, the tax laws say married couples should be treated as though they were a single economic unit - with no distinction between families in which one spouse earns all the money and those where both partners are wage-earners.

Tax experts say it just can't be done without giving way in some area. And the way the tax laws are structured now, it's couples who carry the extra burden.

Take the example of Mike and Joan, each earning $15,000 a year. If they file returns as single persons, their tax is $2,682 each - for a combined total of $5,364. IF they marry and file jointly, their taxable income is $30,000 - and they pay $6,488 in taxes.

Their penalty for getting married: $1,124.

In another example, Fred earns $24,000 and Betty earns $6,000. Filing as single persons, they would have to pay taxes of $5,734 and $576 respectively - for a total tax bill of $6,310. If they marry, their taxes rise to $6,488 - or $178 more.

The "marriage penalty" problem has been around almost as long as the tax code.

During the first half of the century, married persons all were taxed as though they were single. So, couples with only one spouse earning the money paid higher taxes than two-earner families with the same income.

Then, in 1948, the law was revised to allow income-splitting - taxing couples as though they were two single persons each earning the same amount. But that left single taxpayres paying propotionally more.

In 1971, the law was changed again - this time to ease the "penalty" on single taxpayers.Under the new revisions, taxes for single persons no longer would be more than 20 per cent higher than those for couples.

As the law stands now, both single persons and couples are being overtaxed - though in different ways. Single person generally pay more in taxes than a married couple with the same income. But marrieds may more than they would if they were single.

To be sure, tax purists would argue that married couples should be paying somewhat more than they would if they were single. Even if two can't live quite as cheaply as one, they still can live more cheaply per person.

An tax experts question whether the extra $180 a year or so really plays much part in a couple's decision on whether to marry. "Presumably, if there's real love involved," one analyst says, "it'll be strong enough to conquer the extra $180 a year."

Moreover, reducing the marriage penalty could be expensive - at least for the government. A partial solution could cost as much as $1.7 billion in reduced revenues. And any more serious effort could run far higher.

But married taxpayers still are clamoring for greater equity, and policy makers still are hunting for ways to reduce the marriage penalty somewhat.

The Carter administration tried - and scrapped - one proposal: In its tax package of last September, the White House toyed briefly with offering a special deduction of up to $600 for working spouses that would have trimmed the penalty some.

But that idea was jettisoned as too complex and too costly. Instead, the administration hopes to reduce the disparity by replacing the present $35 a person general tax credit and revamping the rate schedule at bit.

Meanwhile, in Washington last week, would-be marrieds suffered another setback when the U.S. Supreme Court turned down a lawsuit that would have challenged the marriage penalty as discriminatory against couples.

The Justice Department had argued that "a marriage-neutral income tax is impossible" and that the government's tax schedule is not unconstitutional, imperfect as it may be.

The court, however, declined any comment on the issue - which may be about all there is to say about redressing this complex bit of tax-law inequity.

As Edwin S. Cohen, a former assistant Secretary of the Treaury for tax policy, told Congress a few years ago, you can't eliminate the marriage penalty without giving up the principle of progressivity in the tax code.

And that may mean more to most American couples in the long run than whether it costs more to file a joint return.