A DELEGATION of the country's governors emerged from a meeting with President Reagan Monday with smiles and a word of caution. The president said he would entertain revisions of his "new federalism" policy along the lines preferred by the governors. But when the governors raised the question of the 1983 budget--a far more pressing concern for them--the president did not reply.

The president's lack of response to their budget concerns did not trouble some of the governors because, as one of them put it, "none of us expects the president's budget to pass"--a view that may have been encouraged by the sympathetic reception the governors received from key legislators earlier in the day. The governors, however, will no doubt remind themselves that whatever the egree of current congressional disaffection with the administration's budget plans, a prolonged stalemate is a real possibility. This would be, in some ways, the worst of all possible outcomes from their perspective.

The president has shown little disposition to compromise on his budget proposals, despite their cool reception on the Hill. His strategy may be to rely on his veto power to forestall action until the fall elections approach. The rush to adjourn could-- as it did last Christmas--force compromise on a package far more to the administration's liking than any that early horse-trading would produce. Even Congress may be glad in the end to be spared the necessity of painful votes on individual budget items.

From the point of view of the states, however, another prolonged budget fight means total havoc. Already far into their fiscal years, states and localities still lack final interpretations from the federal government of what some of last year's budget cuts and legislative changes mean for their current operating budgets. The specter of another set of effectively retroactive cutbacks next winter is enough to paralyze operations in state and local governments.

It is important for all sides concerned to realize now that there are many more than two players in the budget game. This is not a simple contest between Republicans and Democrats--or even between Congress and the administration. The federal budget is part of an intricate system through which services, supports and guarantees are provided to every citizen, business and financial institution in the country. States and localities are important participants in this system, and they need to have a say in changes to be made in the system as well as adequate time to prepare for them.