Americans fear Social Security may go broke, but they overwhelmingly oppose cuts in benefits and would be willing to pay higher taxes to keep the system sound, according to a survey conducted by the Louis Harris polling organization for the National Council on the Aging.

The survey, released yesterday, was based on in-person interviews with 3,427 people of all ages from June 15 to July 31 of this year. It cost about $400,000, nearly all donated by Atlantic Richfield, Exxon, Levi Strauss, Colonial Penn, Bankers Life and Equitable Life.

The results clearly reveal why President Reagan's now-withdrawn demand for major Social Security benefit cuts to counter trust fund financing problems was one of the biggest tinderboxes of his presidency. Key findings:

* Fifty-four percent of all people 18 or over had "hardly any confidence" that Social Security would be able to pay them benefits when they retired, and among those 18 to 54, the figure was 68 percent.

* But 92 percent opposed reducing benefits for those already retired; 85 percent opposed reducing them for future retirees; 59 percent opposed raising the retirement age from 65 to 68; 62 percent opposed cutting out benefits for children of retired workers; 73 percent opposed cutting annual cost-of-living adjustments; and 64 percent opposed using a means test for receipt of benefits. About the only cut favored (by 56 percent) was basing cost-of-living adjustments on the lower of wage or price increases.

* Fifty-one percent favored raising Social Security payroll taxes to strengthen financing (39 percent opposed this), 76 percent favored bringing federal workers into the system and 62 percent favored using general Treasury revenues.

Among people who were working, three-quarters said they would like to continue at least part-time after reaching retirement age.