The big riddle in many corners of "State House America" is why President Reagan and Congress cannot get their act together on reducing the federal budget deficit. The answers do not seem as simple as they did a few months ago.

Last spring, governors and state legislature leaders joined mayors and county commissioners in circling wagons around favorite programs they feared would be scalped in the name of deficit reduction.

The governors, moreover, boasted that they had balanced their budgets with politically painful tax hikes and spending cuts. They offered to share the political heat if Washington wanted to follow suit. They ridiculed the Washington notion that the deficit somehow would shrink if the economy soared along the proper "glide path" of recovery.

Now, many governors and state legislators say that they not only are disappointed with efforts to reduce the federal budget's deficit but are continuing to lose jobs and exports to foreign competition, uncertain about the impact of federal tax revision and fearful of a general economic downturn. They talk of the inaction in Washington with frustration bordering on cynicism.

"What Congress did was, seeing a series of unpleasant choices, they punted," said Florida Gov. Robert Graham (D), "and probably punted until 1987."

Tennessee Gov. Lamar Alexander (R), chairman of the National Governors' Association, said with resignation that he is in "a perpetual state of shock" over the lack of action on the deficit.

Virginia Gov. Charles S. Robb (D) seemed incensed by Reagan's unwillingness to risk any of his abundant popularity on the kind of leadership that Robb contended is necessary to underscore the seriousness of deficit reduction.

Many state officials complain of seeming insincerity in the administration's advocacy of a new federalism, a federalism they contend already has given them more authority but fewer resources and is based on false notions.

In budget battles, the administration asserts that state and local governments are brimming with budget surpluses. White House officials also have justified their tax-simplification plan, whose linchpin is repeal of the federal income-tax deduction for state and local taxes, with the assertion that only a few states -- those with high taxes and many services -- would be hurt.

Both administration assertions were widely challenged at the 11th annual meeting of the National Conference of State Legislatures (NCSL) here last week and the 77th annual meeting of the National Governors' Association a few days earlier in Boise, Idaho.

An NCSL study reported that, despite some generally modest budget surpluses, states are not as well off as five years ago and that state revenues are declining. Eighteen states lowered taxes during the fiscal year that ended June 30, but 25 raised them. Growth in spending was on the decline, and so was some optimism.

"State finances are volatile," the report concluded, noting that an economic downturn could wipe out even the largest budget surpluses. "State budgets reflected extreme concern that an economic slowdown could depress revenues and that large federal aid cutbacks might soon create serious budget problems."

In Oregon, for instance, the economy is expected to produce 18,000 fewer jobs in the next quarter than earlier projected.

"I don't know if people understand how bad it's been in Oregon," said state Sen. Jane Hardy Cease (D). "We look like we're on the verge of an opportunity to build things up, and . . . the federal government may be taking some of that opportunity away."

Several states who rely on the timber, automobile and oil and gas industries are still awaiting recovery as are many where agriculture is an economic foundation.

"We just don't have any lights at the end of the tunnel" in the rural economy, said Mississippi state Rep. Charlie Capps (D).

Unemployment is finally below the national average in Wisconsin, but Gov. Anthony S. Earl (D) said caution is still evident.

"There's an intangible softness there," Earl said. "Nobody is willing to say we've got things righted now, we're on the right track. The old notion of a job for life is surely gone."

Rhode Island state Sen. Michael Flynn (R) said, "Everyone expects the economy to drop off."

Adjusting to what one speaker termed "three Rs" of contemporary municipal finance -- revolt of the taxpayers, recession and reduction of federal aid -- states are keeping a closer eye on the potential time bombs of pension funds and are overhauling tax systems.

The states have learned firsthand that some things touted as fiscal panaceas are of limited help.

In Georgia, for instance, governors have line-item veto power like that Reagan seeks. But in the past 15 years, only one of 40 such vetos affected a major appropriation. The rest were used to express what state Rep. Lauren (Bubba) McDonald termed "the personal displeasure of the governor."

While many state officials said their residents would likely benefit from the reduction in personal tax bills that could result from federal tax simplication, many have lingering uncertainties about tax revision: How will voters behave if state and local taxes no longer are deductible? How accurate are revenue forecasts? What effect will tax overhaul have on different state taxes?

New York state Sen. John Marchi (R), a foe of the repeal of deductibility, dismissed the value of the Reagan tax-revision package, declaring, "This dog won't hunt."

For others, the tax-revision plan simply further clouded the economic picture of the states. And they see the failure to take action on the deficit as symptomatic of a puzzling and debilitating strain of Potomac Fever.

"The closer you get to Washington D.C. ," complained Washington state Sen. Eleanor Lee (R), "the more you get blinders on you."