President Carter sent Congress a new welfare plan yesterday after slashing costs of $5.7 billion a year in place of a $20 billion proposal that died in Congress last year.

Carter, in a message to Congress, said the proposal to overhaul the program of aid to families with dependent children (AFDC) would help rationalize a "crazy-quilt patchwork system" while "improving incentives and opportunities to work and substantially improving the incomes of millions of poor people."

The National Governors Conference greeted the bill warmly and praised its provisions to give $900 million in "fiscal relief" to states.

Secretary of Health, Education and Welfare Joseph A. Califano Jr. told a press briefing that the slimmed-down package is better positioned for passage this year because it has the support not only of Rep. James C. Corman (D-Calif.), who sponsored it last year, but also of House Ways and Means Committee Chairman Al Ullman (D-Ore).

Labor Secretary Ray Marshall said public service jobs sections will be sponsored by House Labor Committee leaders Carl Perkins (D-Ky.) and Augustus Hawkins (D-Calif.). Califano conceded that Senate passage would be difficult because of the long-standing opposition of Senate Finance Chairman Russell B. Long (D-La.) to proposals of this type, but said that if the proposal reaches the floor of the Senate "it will pass overwhelmingly." Sen. Daniel P. Moynihan (D-N.Y.), a welfare expert, said "I will introduce and support the bill."

Last year's bill failed because budget-conscious members of Congress didn't like the $20 billion-a-year price tag. Carter clipped the costs of the new proposal by cutting back the classes of people eligible for new federal welfare minimum income guarantees ($4,700 for a family of four without other income), and by reducing the number of "last-resort" public service jobs for welfare clients from about 1 million to 400,000 new slots. But whether the truncated package can do any better is far from clear.

The new program would become fully operational in 1982. The $5.7 billion added annual cost would be on top of existing costs estimated at about $24 billion in 1982. (These figures are in 1982 dollars.)

Here are some key features:

Families with minor dependent children would be guaranteed a minimum welfare payment (partly in cash and partly in food stamps) at two thirds of the poverty line. For a family of four, the payment would be $4,700 a year-in current dollars-if there were no other income. If the family had earnings the benefits would be reduced. At present, the welfare benefits and food stamps combined are lower than $4,700 in 13 states.

A family with small children and an unemployed father would become eligible for benefits in all states. At present, 24 states preclude welfare to a family with a father present even if he is unemployed.

Welfare applicants would face new, intensive government efforts to find them private jobs, but if such jobs were not available, the government would create 400,000 new public service jobs and training slots at an average of $7,200 a year (in 1979 dollars) pay. Some 170,000 such jobs already in existence would be slotted for welfare families also. By taking such jobs, they would get off the welfare rolls and learn new skills.

A special tax credit for poor people ( $500 a year on the first $5000 of earnings) would be increased to $600 for persons with private jobs, boosting the income of about 6 million people.

Families on the SSI program (destitute aged, blind and disabled persons) living apart from their children or other nonpoor relatives would have their monthly cash welfare payments boosted instead of receiving food stamps, benefiting about 1.6 million people.