Health, Education and Welfare Secretary Joseph A. Califano Jr. yesterday refused to back off his attempt to speed up Social Security payments by many local governments, despite strong objections from 54 senators and many state and local government groups.

About $200 million a year in interest is at stake.

At present, state and local governments are required to hand over the paroll tax to the United States. Only at three-month intervals, whereas any large business must make the payments weekly. The state and local governments collect the money from employe payroll, and invest it in short-term federal securities, collecting interest, which may soon each $200 million a year.

Califano wants them to fork over the Social Security payroll tax proceeds montly instead of every three months. In that way, the Social Security system could invest the money and receive $200 million a year in interest.

A round-robin letter sent to Califano by Sen. Gaylor Nelson (D-Wis.) and backed by Senate Majority Leader Robert C. Byrd (D-W.Va.) and 52 other senators warned Califano to drop his attempt to alter the payment schedule.

Yesterday Califano wrote Nelson that the one-month requirement would still be easier than the one-week requirement to which private businesses are subject and would allow state and local units to earn $50 million a year in interest.