The nation's governors breathed new life into the Reagan administration's "New Federalism" proposals yesterday, saying they had reached a tentative agreement with the White House over key elements of a plan to swap responsibility for major health and welfare programs.

Under the compromise, states would assume primary responsibility for the nation's largest welfare program, Aid to Families with Dependent Children (AFDC), in exchange for a federal takeover of Medicaid. The federal government would also retain responsibility for the costly food stamp program.

The governors stressed that the agreement is a tentative one.

"A compromise has been engineered, but not approved formally by either side," said Gov. Richard A. Snelling of Vermont, chairman of the National Governors Association.

He said "all the major items" of disagreement had been resolved in recent negotiations, and the governors now are waiting only for details on the administration's position on Medicaid.

"The ball is now in their court and we're waiting somewhat impatiently," Snelling, a Republican, told reporters after a meeting with 12 other governors.

The White House refused to confirm Snelling's statements. But Richard S. Williamson, the presidential assistant for intergovernmental affairs, said, "We're encouraged. Everything is on track."

An endorsement by the governors is considered critical to enactment of any federalism proposal on Capitol Hill.

The compromise announced yesterday alters the New Federalism initiative that President Reagan spelled out in January in several major ways, according to sources.

Reagan proposed a federal takeover of Medicaid in exchange for state assumption of responsibility for food stamps and AFDC. The federal government currently finances about 55 percent of Medicaid and AFDC and all of the food stamp program, which is estimated to cost almost $12 billion this year.

The compromise, sources said, would "remove food stamps from the New Federalism basket" in exchange for state assumption of more categorical programs in health, transporation and education. Reagan originally proposed shifting about 40 such categorical programs to the states, to be financed by a $28 billion temporary federal trust fund.

The compromise, sources said, would increase the number of categorical programs shifted to the states to about 50, and reduce the size of the trust fund, but the states would not take over food stamps.

A minimum national standard would be set for AFDC payments, and a special "safety net supplemental fund" would be established for that purpose.

The idea is that the fund would provide a cushion for states suddenly hit with high unemployment, like Michigan, and chronically poor states, like Mississippi.

The new plan also includes a provision to prevent the federal government from lowering food stamp allocations when welfare benefits are raised.

Snelling said he will poll all governors once the elements of the compromise are confirmed by the White House. Several other governors indicated a deep concern about the Medicaid provisions.

The range and amounts of benefits Medicaid recipients now receive vary greatly, with big industrial states like New York, Illinois and California providing the most generous services. The governors' concern is that the administration might set national standards so low that states would feel compelled to supplement them to maintain current benefit levels.

The governors also adopted a formal statement urging rapid action on the federal budget. The statement said projected deficits "would further aggravate our economic chaos" and urged that no part of the budget--including Social Security and defense--be considered "untouchable."