Several leading Democratic governors, breaking ranks with Gov. Mario M. Cuomo (D) of New York and an almost solid front of state and local officials, have indicated their willingness to accept partial repeal of the deduction for state and local taxes as a price for overall federal tax revision.

But the Reagan administration and key Republican governors, insisting that the deduction is primarily a subsidy for a few wealthy taxpayers, so far have flatly rejected any compromise on the president's proposal to eliminate it entirely.

The latest compromise overture came last week from Kansas Gov. John Carlin (D), president of the National Governors' Association.

"We are aware that in order for the object of tax reform to be accomplished that we can't ask for total protection," Carlin told the Senate Finance Committee. "But there are ways in which we can accommodate your need for revenue and still protect the basic thrust of deductibility and the system of federalism."

Carlin's conciliatory tone was echoed by Gov. Richard D. Lamm (D) of Colorado. The U.S. Conference of Mayors, the National League of Cities, the National Association of Counties, the National Conference of State Legislatures and the National School Boards Association held the line in favor of retaining the deduction.

Pennsylvania Gov. Richard L. Thornburgh (R), chairman of the Republican Governors' Association, was just as firmly on the other side. "My view is: is what the president's proposed better than what we have today? And my answer is a resounding yes," Thornburgh said.

Mitchell E. Daniels Jr., the White House director of intergovernmental affairs, also ruled out any compromise. "The first issue is fairness and the second is practicality," Daniels said in an interview. "You can't have meaningful tax reform without the revenue now rebated through deductibility."

The money that the Treasury would recover by ending the deduction, estimated at $37 billion by the Joint Committee on Taxation, is the single largest revenue-raiser in the tax revision plan, which Reagan has promised will be "revenue neutral."

Cuomo, a possible presidential candidate in 1988, has emerged as the most prominent critic of Reagan's plan to repeal the deduction. The New York Democrat argues that such repeal would lead to a "tax on a tax," hurt millions of middle-income Americans and "punish" states, counties and local school districts trying to raise money to maintain or expand services.

New York stands to lose more than any other state if the deduction is ended. But Cuomo's argument has been echoed by several unlikely gubernatorial allies -- including Gov. Ed Herschler (D) of Wyoming, which would lose the least if the deduction ends, and Gov. Thomas H. Kean (R) of New Jersey.

In Massachusetts, where Gov. Michael S. Dukakis (D) has reserved judgment, a study of the Reagan tax revision plan found that although middle-income taxpayers generally would be hardest hit, the state would not be "devastated." The loss of revenues from repeal of the state and local deduction would be offset by gains from other parts of the tax revision package. By 1990, the report concludes, the state would have a net reduction of $108 million in its federal tax bill.

The Democratic governors searching for a compromise are concerned, however, about how much of the burden of tax revision winds up on their shoulders.

State and local officials also complain that they already have borne a disproportionate share of federal budget cuts. The federal government, they say, is shifting more program responsibilities to them while creating an atmosphere that could lead to "tax rebellions" that would cripple efforts to fund those programs in the not-so-immediate future.

They also say the administration already caved in to special interests by abandoning some of its original tax reform proposals, including elimination of fast tax writeoffs for oil and gas drilling costs. "They're basically taking our resources and giving them to the oil and gas industry," Arizona Gov. Bruce Babbitt (D) said.

The governors' organization, which is officially on record in opposition to repeal of the deduction, begins its annual summer meeting Saturday in Boise, Idaho. It is not clear whether the governors will try to hammer out a new position there.

"Part of the problem is that governors are all over the place," one aide said, and "a lot of steam's gone out of tax reform, period."