By 57 to 24 percent, Americans support the steps President Carter is taking to restore the value of the dollar abroad. Perhaps even more significant, by 56 to 27 percent, they are prepared to continue to back the stringent measures to shore up the dollar and slow inflation, even if it means a recession.

This commitment to a program that involves raising interest rates and may slow economic groth and increase unemployment must be taken as a measure of the desperation Americans feel about inflation.

A clear majority is now convinced that there is no way to beat inflation without making some economic sacrifices. What people also are saying is that unless we are prepared to suffer a short recession in the near future, inflation will continue to soar and ultimately result in a deep recession or even a depression.

These findings from a recent ABC News-Harris Survey of 1,200 adults across the nation also reflect the public's underlying frustration with a national leadership that somehow did not believe that people would respond to tough medicine.

Approval for Carter's dollar policy comes from a wide spectrum of the population. For example, self-styled conservatives back his policy by 55 to 23 percent, middle-of-the-roaders support him by 61 to 23 percent, and liberals back him by 62 to 24 percent.

As for supporting the program if it is likely to bring about a short recession, there are some significant differences:

Professional people back his policy of risking a recession by 72 to 22 percent; those with incomes of $25,000 or more support his plan by 73 to 18 percent, and the college educated back him by 69 to 19 percent.

However, less affluent and less privileged people are less willing to risk recession. Among those earning $7,000 or less, support dwindles to 34 to 31 percent. Among black, it is 41 to 39 percent. Among union members it is 51 to 35 percent.

The major implication of these findings is that Carter will have to rely heavily on whatever loyalty and support he has as a Democratic chief executive to get the "gut vote" of his own party to go along with him.

On Nov. 3 and 4 the survey asked the cross section:

President Carter has announced a series of measures to halt the drop in the value of the dollar abroad, involving higher interest rates and agrement with th Japanese, German and Swiss national banks to support the dollar. These steps may slow down the growth of the economy and cause higher unemployment, but they could also reduce the rate of inflation. Do you favor or oppose this policy? (TABLE) Total(COLUMN)57%(COLUMN)24%(COLUMN)30% Political Philosophy(COLUMN)(COLUMN)(COLUMN) Conservative(COLUMN)55(COLUMN)23(COLUMN)32 Middle-of-the-road(COLUMN)51(COLUMN)23(COLUMN)16 Liberal(COLUMN)62(COLUMN)24(COLUMN)34(END TABLE)

Some economists are saying that this new policy will probably cause a short recession next year. Do you approve or disapprove of the new measures to stop the decline of the dollar and reduce inflation even if they are likely to cause a recession? (TABLE) (COLUMN)Favor(COLUMN)Oppose(COLUMN)Not Sure Total(COLUMN)56%(COLUMN)27%(COLUMN)17% Political Philisophy(COLUMN)(COLUMN)(COLUMN) Conservative(COLUMN)55(COLUMN)27(COLUMN)18 Middle-of-the-road(COLUMN)59(COLUMN)27(COLUMN)14 Liberal(COLUMN)59(COLUMN)29(COLUMN)22 Education(COLUMN)(COLUMN)(COLUMN) 8th grade(COLUMN)33(COLUMN)37(COLUMN)36 High School(COLUMN)47(COLUMN)34(COLUMN)19 High School(COLUMN)47(COLUMN)34(COLUMN)19 College(COLUMN)49(COLUMN)19(COLUMN)12 Income(COLUMN)(COLUMN)(COLUMN) Under $7,000(COLUMN)43(COLUMN)31(COLUMN)26 $7,000-$14,999(COLUMN)53(COLUMN)30(COLUMN)17 $15,000-$24,999(COLUMN)62(COLUMN)27(COLUMN)11 $25,000 and over(COLUMN)73(COLUMN)18(COLUMN)9 Occupation(COLUMN)(COLUMN)(COLUMN) Professional(COLUMN)72(COLUMN)22(COLUMN)6 Executive(COLUMN)70(COLUMN)24(COLUMN)6 Proprietor(COLUMN)58(COLUMN)23(COLUMN)19 Skilled labor(COLUMN)57(COLUMN)31(COLUMN)12 White collar(COLUMN)48(COLUMN)31(COLUMN)21 Race(COLUMN)(COLUMN)(COLUMN) White(COLUMN)57(COLUMN)26(COLUMN)17 Black(COLUMN)41(COLUMN)39(COLUMN)20(END TABLE)