You had only to be there when Alexander M. Haig Jr. addressed the National Governors Conference to see what a dreadful, although not irretrievable, mistake the president has made on the "New Federalism."

When the secretary of state finished his rambling remarks, Arkansas Gov. Frank White (R) asked Haig if he were having any kind of "meaningful dialogue" with Cuban President Fidel Castro.

What the governor was telling the secretary in the nicest possible way is that he does not wish to play host at Fort Chaffee to another host of Cuban refugees. He's had it with machete fights, camp riots, stabbings.

White understands infinitely better than the hawks in the White House that bad relations with other countries produce refugees -- and a fearful drain on welfare funds, food stamps and all of the other programs that President Reagan proposes graciously to give back to the states.

As Colorado Gov. Richard D. Lamm (D), who had a bout with the consequences of our Southeast Asian policies, thousands of Vietnamese refugees, observed delicately, "We have compassion fatigue."

The obvious solution is to keep social programs in the hands of the federals and to defederalize foreign policy.

Under this new New Federalism, every state would be the sole agent to deal with a preferred, or assigned, foreign country.

The State Department would close down and ambassadors would go to state capitols, with such relief to the parking problem here as to justify the whole undertaking.

You can be sure that with Arkansas handling Castro in a focused, non-ideological way, and with a franchise on Cuban cigars to balance its budget, things would go more smoothly. Arkansans could learn the conga, and Castro could be taught square-dancing and to keep his undesirables at home.

Florida Gov. Robert Graham (D) also understands better than Alexander Haig how ruinous it is to see everything as a Soviet plot. Every morning, Graham gets up and picks up a new tide of Haitian boat people off of his beaches.

The federals have been of absolutely no help, so Graham in desperation went to Port-au-Prince to reason with the locals. He has a sharp interest in making it possible for Haitians to stay home instead of setting out for Florida in leaky boats. Give Haiti to Florida.

Another natural pairing springs to mind. Michigan is going under because of Japan. The U.S.-Asia Institute has made a breathtaking offer of $10 billion to revive American industry.

Before we get into a hard-breathing debate about the shame and humiliation of it all, let Michigan Gov. William G. Milliken (R) grab the money for unemployment compensation and start negotiating with the Japanese. Bring them over, or send Detroit's unemployed to Tokyo for a refresher course in how to build cars that people want to buy. Soon, instead of threats of trade wars, you would have teahouses in Hamtramck and bowling lanes on the Ginza.

Louisiana and France both speak French and have the Napoleonic Code. Acrimonious exchanges about French participation in the Soviet gas pipeline would give way to more impassioned, but less dangerous, discussions about the best way to make bouillabaisse.

California would take on China, which badly needs mellowing-out and, as China gropes toward sex and other amenities, it could use hot tubs, encounter sessions and instruction in how to get in touch with its feelings. A little spaciness would help in its relations with the outside world.

Indiana is a natural for the Soviet Union. Both are deeply suspicious, intolerant and overarmed--Indiana's parks bristle with cannon. Matching paranoias might cancel each other out.

More popular countries, such as Britain and Ireland, would probably have to be raffled off, and the hard to love, such as Albania and North Korea, might have to carry a tax rebate to be taken up. If any state decided, incidentally, to go to war, it would have to raise its own army or make its own nuclear bomb.

Speaking of war, the federals appear to be dying for hostilities with Nicaragua. Let us give it to Wisconsin, which also has been plagued with political extremists. Having given us the LaFollettes and Joe McCarthy, Wisconsin would understand Nicaragua's identity crisis.

The beer capital of the world could begin by sending a million or so cases of its finest brew to Managua. It would, at the very least, make the Sandinistas sleepy and possibly cause them to act more like burgomasters than commissars.

El Salvador needs Vermont, a calm, beautiful place. Its senator, Patrick Leahy, has already gotten into an admirable row with San Salvador's security chief. Vermont could introduce the town meeting, which El Salvador needs so much more than any additional arms.

This is only a start. Let us hear no complaints that chaos would result under the new New Federalism. Surely, 50 foreign policies are better than none.