Sixteen years ago, in the wake of a midterm election in which voters rebelled against the inflationary side effects of the newly enacted Great Society programs and the newly expanded Vietnam War, a group of Democratic governors gathered in White Sulphur Springs, W. Va.

It had been a rough election for the Democrats. Eight governorships had fallen to the Republicans and House losses were heavy. The governors' chairman, Iowa's Harold E. Hughes, came out of the caucus to declare their belief that if their party continued the same policies for another two years, it would be turned out of office. "If Lyndon Johnson had been running this year," Hughes told reporters, who were then unaccustomed to his candor, "he would have had a very rough race."

The message to the White House from the Republican governors who met in Kansas City last week was less pointed -- but just barely. Another midwestern governor, as big and as blunt as Hughes, Illinois' James R. Thompson, was the spokesman. And the way he put it was this: the 1982 election was "a cry for help," and those in power "have two short years to respond."

Thompson's message was echoed and amplified by the others who gathered for the gloomy roundtable. They came together -- some victims, some shaken survivors -- intending to lick their wounds, but not to light the fires of rebellion. But, like others who have been confronted with the seeming indifference of the Reagan White House to the import of the recent election, they moved quickly from shocked disbelief to barely suppressed anger.

Richard S. Williamson, the president's assistant for intergovernmental relations, told them Ronald Reagan regarded the election as "a wash." It is a phrase that has been repeated endlessly by Reagan aides since Chief of Staff James A. Baker III employed it on election night. But it was not the most felicitous expression to use to a group that had just seen its numbers reduced by one-third, from 23 to 16.

Nor were the governors persuaded when presidential pollster Richard B. Wirthlin told them that there was no problem confronting their party "that can't be solved by a 3 percent growth rate."

Like the Democrats of 1966, who said through Hughes that their losses were "basically a trend from the national level -- anti-administration," Thompson and the others attributed their casualties to national issues.

V. Lance Tarrance, the young Houston pollster who worked in many of the governors' campaigns, pointed out that "they got exactly the same 43 percent of the vote in their races as the House Republican candidates did. This was a national election."

Tarrance also made the observation that the election had roused the governors from their long period of political lethargy. As a group, they played almost no part in the selection of Reagan as the 1980 nominee. But now, as Tarrance said, "They are ready to raise their voice in the Republican Party and say to Republicans in Washington, 'If you don't understand what's going on in the country, we do.'"

One of the things the governors understand is that, as Thompson said, "putting people back to work has to be our top priority." Another is that the Reagan administration has foolishly and perhaps fatally antagonized major voting groups: farmers, small-business people, union members, the elderly, women and (most often cited) minorities.

Texas Gov. William P. Clements, defeated for reelection, told how he was overwhelmed in the barrios by a Democratic challenger who had opposed extension of the Voting Rights Act and criticized bilingual education. Pennsylvania Gov. Dick Thornburgh told how his margin had been sliced in Philadelphia black wards he had carried four years ago, even though his Democratic opponent was a stranger to those voters and to the civil rights cause. Thompson himself told how the outpouring of black votes in Chicago had almost defeated him.

"We have to reach out to blacks and Hispanics," Thompson said. "They voted straight Democratic, against liberal Republicans, moderate Republicans and conservative Republicans, even when they didn't particularly like the Democrats. They were sending a message to someone, and that message must be heeded."

There was some muttering among the governors about Reagan's bypassing their meeting and making a speech, instead, to a savings and loan convention in New Orleans. In that speech, Reagan vowed to continue on the same path, accelerating the defense buildup, cutting taxes across the board, and attempting to close the huge deficit gap by slashing domestic programs.

Reagan's New Orleans speech was clear proof that the message of Kansas City has not reached him. But the lesson of White Sulphur Springs is that such warnings from the governors can be ignored only at the president's peril.