In the FDR era that we now commemorate, one of the most enduring, and endearing, public figures was the mythical "Senator Claghorn," that pompous, ignorant, loud-mouthed gasbag who entered our living rooms weekly thanks to Fred Allen's radio show. He was, in the mind of millions, the instantly recognizable stereotype of a servant of the people, Washington style.

Succeeding years brought a different type of fictional public figure. Instead of Senator Claghorn, posturing and bellowing in the halls of Congress, we came to know the equally loud and swaggering, pot-bellied, cigar-chomping sheriff. He became, to millions, the familiar representative of the people, local style.

But where the senator held a certain lovable charm mixed in with all his bombast and deceit, there was nothing attractive about the sheriff. With his dark glasses and jowls, cattle prod and nightstick, handcuffs and revolver, he was fearsome, a lout and a brutal bigot who lacked the slightest bone of compassion or fairness.

The sheriff personified public attitudes about the workings of American government on the state and local level. Look not to those statehouses and legislatures and city halls for the flowering of our system. They are, everyone knows, the home of the Yahoos, of petty politics, graft, officials in the pay of the interests, of representatives of the people who do not practice democracy and of law officials and lawmakers who do not enforce and draft the law equally for all.

Thus, it comes as no surprise that the immediate overall reaction of Washington, which always knows best, to the president's plan to turn back federal programs to the states and localities is one of dismissal.

There are certainly problems aplenty in this proposal, central among them the concern for national standards and the principle of fairness to every citizen being applied equally everywhere. But the idea deserves better than that. So, too, do the states and localities. Not all their old problems and practices have been solved, but many of the stereotypes about them are no longer valid.

One of the dramatic changes of the last generation involves the health and vigor of state and local governments and the way citizens have been responding to them.

In the past the statehouses earned their public contempt, but in recent years they have been characterized by legislative innovation and reform. The quality of state legislators has changed. Their assemblies are no longer as dominated by the farmer-lawyer combines of the past. More women, more blacks, more suburbanites fill their ranks, and professionalism and pay have increased notably.

Nor are the statehouses in the backwater of American politics and government these days. Across the country new state programs in health, criminal justice and personnel procedures have been implemented. Laws compelling open government sessions have been enacted. Codes of ethics have become more common, and numerous progressive measures have been enacted into law in many states without attracting national attention.

The words of Vermont Gov. Richard A. Snelling, chairman of the National Governors Association, are worth repeating. Writing in The Wall Street Journal, he says:

"State and local governments have changed tremendously since the 1960s, as any objective analysis would disclose. Reapportionment has cured our worst faults, and no patron of federal power can any longer claim automatic moral superiority for the Congress in terms of representing the people. Indeed, while blacks, for example, remain underrepresented at all levels of government, they are a larger percentage of state legislators than of Congress, and in many cities they dominate important government offices . . . . "

Others make the point that today virtually every state in the country spends more of its resources on society's outcasts than does the federal government, whose elected officials can take credit for keeping America collectively strong through defense spending and personally secure through Social Security payments as their main uses of the tax dollar.

They also bristle at the common kind of criticism that singles out the "bad" state or states as evidence that the barrel is filled with rotten apples and must be discarded in favor of a federally imposed one from Washington.

And they raise another hard question about the changing economic conditions in which the nation now finds itself: is the federal government really so rich anymore? As one person who works with the governors asks: "What is the alternative to decentralizing but to send ever-diminishing amounts of federal aid through a system that dissipates resources through overly ambitious and misplaced priorities and masses of red tape?"

So, at least, the stereotypes about state performance ought to be discarded, and, it would be hoped, a more serious debate about the tradeoffs of responsibilities between the federal government and the states begins. In no sense does that mean President Reagan's truly bold approach is the best. Nor does it mean his approach, as presently constituted, isn't fatally flawed.

Here, the views of another governor are instructive.

Gov. Bruce Babbitt of Arizona came out, as he says, of a liberal, activist, Democratic political background. He was one of those who implemented the Great Society reforms during the Lyndon B. Johnson heyday of federal ascendancy, who went south and put progams and grants in place. Today, he says he still believes that important deeds were accomplished then, but he also says he holds serious doubts about some of the federal actions.

"I can't help but wonder how it was we were so casually building pipelines from Washington to community groups then," he remarked, during a lengthy telephone conversation the other day. "In effect, we were bypassing the normal political channels vested with the power to govern. We were ignoring the governors' views. We didn't deal with them."

His views changed when he returned to Arizona and dealt first-hand with the heavy hand of federal bureaucracy and federal regulations, many of them stupid and stultifying. Both as attorney general and then as governor of his state he experienced the frustration of attempting to deal with state agencies ostensibly under his control but which in fact acted as regional adjuncts of federal agencies. They were far more responsive to Washington's dictates than to his.

Babbitt says he welcomes a new relationship between the states and Washington, if such can be achieved. In fact such must be achieved. But he also expresses concern echoed by many others.

"Ultimately, it seems to me what you have to do is try to analyze what programs are invested with a national interest," he says. "I take issue with the president's approach, because sometimes he sounds as if he wants to dump everything overboard. Just have the federal government print money and raise armies. That's not adequate."

There exists, he adds, something more than a political-economic issue. At bottom lies a moral question. It centers on the way in which a nation attends fairly and uniformly to the needs of the less able of its citizens. In the area of health and welfare, both are and should remain federal responsibilities.

Many questions remain about the proper workings of the tangled federal-state relationship. This opening phase of the discussion may well be intended, as alleged, to be a political diversion from the pressing needs of the moment. In the long run, though, the nation has to fashion a better way of doing its business of governing at all levels. Let that debate, the real one, begin.