The Office of Management and Budget has drafted a plan to penalize the states up to $1 billion a year starting in fiscal 1983 unless they reduce overpayments and eligibility errors in the nation's three largest welfare programs, sources said yesterday.

The plan would lay the entire cost of errors directly on the states, helping reduce the federal deficit and forcing the states to tighten their programs.

The plan, which is certain to face opposition from many of the nation's governors and local officials, goes far beyond any similar penalty proposal previously considered.

It involves the Medicaid, food stamp and Aid to Families with Dependent Children programs, all of which are funded in whole or part by the federal government but which are administered by the states, with the federal government reimbursing them later for eligible costs.

Under the plan, sources said, the federal government would refuse to reimburse the states for erroneous benefit payments exceeding 3 percent of a state's total program outlays. This would mean big cuts in federal payments, since the latest published national average error rates were 5.2 percent for Medicaid, 10.6 percent for food stamps and 8.3 percent for AFDC.

While the federal government has previously set targets less stringent than the OMB's for reduction of error rates, so far it has not cut off payments to states with high rates.

Sources said that under the plan, the allowable error rate would drop from 3 percent in fiscal 1983 to 2 percent in fiscal 1984, 1 percent in fiscal 1985 and zero in fiscal 1986.

This means that, starting in fiscal 1986, the states would have to foot the entire bill for any payments made in error. This bill could be fairly large in some states; total outlays are $32 billion in the federal-state Medicaid program, $11.4 billion in the all-federal food stamp program and $14 billion in the federal-state AFDC program.

A spokesman for the National Governors Association said, "Sanctions are not the answer. We are working hard, have made some progress and are continuing to work to bring down errors. The problem is not state inaction but the need to simplify programs and administrative requirements."

Congress three years ago adopted an amendment, sponsored by Rep. Robert H. Michel (R-Ill.), requiring the states to cut their AFDC and Medicaid error rates to 4 percent in steps by the end of 1983 or face penalties.

There is considerable dispute in the welfare community about whether it is cost-effective to try to push error rates down much below 4 or 5 percent.

However, some big states with extensive programs have relatively low Medicaid error rates; for example, New York had only 2.6 percent in the latest published figures and California 3.5 percent.

For Medicaid, the latest published figures show error rates of 9.2 percent for Maryland, 4.4 percent for the District of Columbia and 1.6 percent for Virginia. For AFDC, the figures were 12.7 percent for Maryland, 14.3 percent for the District, and 5.4 percent for Virginia.