The nation's governors acknowledged that the fiscal health of the states has improved markedly since the recession of 1982, but warned yesterday that they will oppose sharp cuts in federal aid to state and local governments unless the defense budget and other programs share the sacrifice.

The governors, who began arriving for the winter meeting of the National Governors' Association, also took issue with administration claims that the states can absorb another round of cuts in federal aid because they have built significant surpluses since the recession.

Saying Reagan's budget doesn't "realistically address" the deficit problem, they challenged Congress to set aside the president's budget and put together a deficit-reduction package that includes cuts in state and local aid, less money for defense than Reagan wants, and possibly cuts in cost-of-living increases for Social Security recipients.

"We're not playing any games back here," said Kansas Gov. John Carlin (D), chairman of the governors' association. "We are dead serious, and we're willing to . . . support anybody in Congress and the administration who's also willing to take a tough stand."

Carlin said the only area that should be exempt from cuts are federal programs for the poor.

The governors' three-day meeting will include sessions with the president and with top congressional budget writers. The deficit, tax simplification and the problems of beleaguered farmers are the top items on the agenda.

"We are not coming to Washington . . . hat in hand and saying, don't cut any of these programs that affect the states," said Virginia Gov. Charles S. Robb (D), who headed a task force that examined the states' budgetary needs. "We're saying . . . we expect continued cuts in those areas, but we don't expect to have the only significant cutting coming in those areas that directly impact the states without addressing . . . that you have to make real inroads in reducing the deficit or you're simply passing the buck."

Robb said if a Congress can't reduce the deficit enough with spending cuts alone, he would rally behind President Reagan if he asked for a tax increase.

Robb said the states "are better off" fiscally than two years ago, when states were forced to raise taxes, cut spending, or both, to balance their budgets during the recession. But he said the "great pool" of state surpluses the Reagan administration talks about is "simply not there."

The Reagan budget calls for a $10 billion cut in aid to state and local governments. The governors' association said that, if Reagan's proposals were adopted, states would be hit harder between now and fiscal 1988 than they were during Reagan's first term.

At the same time, Robb said, the states deferred spending in a number of areas during the recession that require significant additional expenditures in the years ahead.

Still, Robb and Carlin emphasized that the states' chief executives want to see significant progress on cutting the deficit, even if that means reduced aid from Washington to the states. "Defense spending has to be subjected to the same accountability as the rest of the budget," Robb said.

Meanwhile, Democratic governors met privately yesterday to thrash out a controversy over the creation of several new policy groups inside and outside the structure of the Democratic National Committee.

Paul G. Kirk Jr., the new DNC chairman, has proposed a Democratic Policy Commission within the DNC to help the party rebuild its image. But Robb, Arizona Gov. Bruce Babbitt (D) and Rep. Richard A. Gephardt (D-Mo.) have decided to set up their own group, called the Democratic Leadership Council, outside the DNC structure. Kirk opposes the Robb group, saying it will undermine his efforts to patch up the wounds among Democrats.

The Democratic governors approved a resolution from South Carolina Gov. Richard W. Riley (D), which endorsed by name the Kirk group, but which also "welcomes" efforts by other Democrats to rebuild the party.