THE NATION'S governors will be voting today on a resolution calling on Congress and the administration to modify budget priorities and reduce the menacing size of future deficits. The debate over this measure reminds the president that his fight over the budget is not simply with House Speaker Tip O'Neill but with almost every other politician in America.

The bipartisan proposal was developed by the executive committee of the National Governors Association, now meeting here. It is notable not because it calls for a massive shifting of priorities or offers any breathtakingly new insight into how to control the budget. The governor's committee simply looked at the numbers and concluded that without some restraint on defense spending and some effort to rebuild the tax base, the nation is headed for deficits that will be good neither for state treasuries nor for the nation's economic health.

The governors' plan is not a radical document. It recognizes, as the administration does not, that further reductions in basic support for the poor are intolerable. It also calls for less severe cuts than the administration wants in the purchasing power of state and local grant programs and other discretionary programs. Medical insurance and retirement programs are targeted for significant cuts, but no plan for achieving those savings is suggested. Defense spending would be restrained--but it would still outpace inflation by 3 to 5 percent a year over the next five years.

Even with those savings--and reforms in Social Security--a substantial increase in taxes would still be needed to meet the governors' goal of reducing the federal deficit to $90 billion by 1988. That may not seem like much of an accomplishment. But it drew praise from Senate Budget Committee Chairman Pete Domenici and Finance Committee Chairman Bob Dole.

The major threat to the adoption of the proposal by the governors today does not come from Republican governors, most of whom seem genuinely shaken by the prospect of huge deficits. It comes from liberal Democratic governors who feel that the resolution does not go far enough in redirecting the administration's priorities. Whether or not the resolution passes, the governors--from both parties and all regions of the country--have made it clear that President Reagan's budget enjoys very thin support.