BY 66 to 28 percent, the American public favors reducing the maximum federal tax on capital gains from 49 to 35 percent. A measure that would accomplish this has been passed by the House Ways and Means Commitee as part of the general federal tax cut bill.

The capital gains issue has been a major stumbling block for President Carter in his efforts to obtain a tax cut this year. Rep. William A. Steiger (R-Wis.) has advocated that the maximum capital gains levy be reduced to 25 percent, which was the maximum rate for several years.

THe president first announced that he would veto any tax cut bill contained capital gains tax relief. His contention capital gains tax relief. His contention has been that cuts in the maximum capital gains tax help the rich more than the average investor.

The arguement that appears to carry the day for capital gains tax reduction is that "in order to get the economy going again, it is important to provide incentives for people want to invest their money through measures such as a capital gains tax reduction." A lopsided 70 to 19 percent majority agrees.

In contrast, by 50 to 33 percent, Americans agree with Carter's claim that " the small investor would not get more than two bits from a capital gains tax cut."

The current public reactions is similar to that in 1972, when Sen. George McGovern of South Dakota, the Democratic presidential nominee, foavored an income maintenance plan that would have taxed people earning over $12,000 in order to help those earning less. The overwhelming reaction against the plan revealed that a majority of those making under $12,000 opposed the measure because they could foresee the day when they would be earning more.

The basic appeal of Steiger's proposals stems from the fact that many more people can picture themselves in a situation where they could be eligible for capital gains than they feel that such financial gain limited to a relatively few very wealthy individuals. The Democratic-controlled Ways and Means Committee tried to meet the Republican challenge by coming up with a maximum tax of 35 percent. President Carter has threatened to veto that compromise.

Any capital gains tax reduction to come out of Congress is certain to be part of a larger tax-cut bill. And the chief provision of such a tax cut would be a lowering of federal income taxes on individuals. In this latest Harris Survey of 1,238 adults nationeide, by 75 to 17 percent a majority favors a $10 billion federal income tax cut for individuals.

In addition, the legislationis expected to contain a cut in business taxes of as much as $5 billion. The public now favors such business tax cuts by 57 to 32 percent.

If Carter were to veto a capital gains tax cut, he would appear to be reneging on his promise to give people some federal income tax relief this yearor early next year.