The U.S. tax code gives working couples a cash bonus for living in sin, Sen. Charles McC. Mathias Jr. (R-Md.) and Rep. Millicent Fenwick (R-N.J.) charged recently as they kicked off a new champaign to end the "marriage penalty."

According to figures released by Mathias, if two swinging singles are living together and making $10,000 a year each, they pay taxes as single persons and their combined federal income tax bill for 1979 will be $2,354.

But if they get married, Mathias said, they will be "shocked to learn that . . . their tax liability would increase dramatically" to $2,745.

For a higher-income couple, the "penalty" for marrying would be worse. If each earned $20,000 their combined federal tax for 1979 if they stayed single would be $7,674, but if they got married it would jump to $9,366.

This "quirk in the tax code" applies when both partners work and have income. Not only does it discourage young couples from marrying and undermine "our longstanding social objective of shoring up the American family," said Mathias, it makes it profitable for a two-earner married couple to "save money by divorcing and simply living together."

Mathias and Fenwick want to abolish what Mathias has called a "sin subsidy" by allowing each married person to file a separate tax return based on individual income and calculated on the same tax tables used by single persons.

In this way, a married couple with combined annual income of $20,000 derived equally from each partner would pay the $2,354 "singles" rate instead of the $2,745 "married couple" rate.

Sen. Harry F. Byrd Jr. (Ind.-Va.), chairman of the Senate Finance taxation subcommittee, has promised hearings on the issue. And the Treasury, without endorsing any proposal, has indicated it is sympathetic to the concept of easing some of tax pain for married couples.

But the price tag in lost tax revenues is a big one: at least $4.8 billion a year for the Mathias-Fenwick bill, according to a tentative estimate from the Join Taxation Committee of Congress. However, some people believe that is a very low estimate.

And a more modest proposal - a plan by Sen. Mike Gravel (D-Alaska) to allow married couples an extra deduction of up to $2,000 - has a big price tag too. It would cost the Treasury up to $3.5 billion a year.

Moreover, the issue isn't quite as clear-cut as it initially seems. Tax experts have been stewing over the problem for at least 10 years, ever since the tax code was changed to reduce the "single penalty" and instead ended up with a "marriage penalty."

A recent Treasury analysis sent to Gravel outlines the difficulty: there are four basic principles of taxation accepted by Americans, but there is no way to combine all four in a single tax system since they are contradictory.

One principle is "progressivity," namely, the higher the income, the higher the rate of tax. Another is "aggregation," that the income of a married couple should be aggregated to determine family income for tax purposes. The third principle is that there shall be no penalty for being married, and the fourth is that there shall be no penalty for remaining single.

The present "marriage penalty" results from the fact that a married couple's income is aggregated and then subjected to a progressive tax.

One Capitol Hill tax expert said the Mathias-Fenwick approach could help solve the "marriage penalty" but only at the expense of other categories of taxpayers.

For example, at present a married person with a $20,000 salary and a nonworking spouse has the same federal tax liability ($2,745) as a married person with a $10,000 salary and a spouse also making $10,000. Aggregate salary in each case is the same, and the tax is the same.

But under the Mathias proposal, the first family would still pay $2,745 but the two-worker family's tax bill would be cut to $2,354.

Moreover, a single worker living alone today and making $20,000 has a tax bill of $3,837, substantially more than that of a married couple with the same income. That is the "singles' penalty," which was reduced 10 years ago, helping to create the "marriage penalty." Mathias' proposal would again enlarge the difference.

Whichever way you turn, someone is going to be paying proportionately more and may consider the change unreasonable.

However, Mathias is weighing in on the side of "the people who have undertaken the care and raising of our children. Clearly, they should not be punished by our tax system," he said.