For some time now, the 1988 pre-nomination strategies of Vice President George Bush and Rep. Jack Kemp (R-N.Y.) have seemed clear: Bush would run as the institutional and personal successor to Ronald Reagan while supply-sider Kemp would offer himself as Reagan's ideological and spiritual successor.

That seemed fair in both cases. After all, it had been Ronald Reagan's 1980 advocacy of Kemp's tax-cut idea that enabled Reagan, and the Republicans, to appeal to blue-collar voters, not with dour lectures about cold showers and root canal work but with confident enthusiasm for a brighter tomorrow. Kemp's special brand of nonestablishment Republican populism, combined with the New Yorker's own energetic accessibility and discipline, looked formidable for 1988.

But in the recent House battle over tax reform, Republican "populism" turned out to be mostly myth. Opposing the Reagan- backed Democratic bill to provide the largest ever single-year cut in individual and corporate rates, "populists" such as Newt Gingrich (R-Ga.) reverted to the traditional GOP script of Gloom and Doom, predicting the loss of 1.5 million American jobs. And Jack Kemp, a leading choice to succeed the Great Communicator, looked a lot more like the Great Hesitator, eventually supporting the bill after he had publicly blasted it, the process by which it was written and the administration's part in that proc There was a plausible economic argument to be made in opposition to the Democratic tax bill the president backed. That argument was made by two respected Republicans, Reps. Bill Frenzel of Minnesota and Dick Cheney of Wyoming, neither of whom has ever presented himself as a Joe Six-Pack Republican. That's how populist Republicans had been advertised: as a shot-and-a-beer kind of guy with the guts to take on liberal elitists on such issues as busing and school prayer, and to take on those country-club conservatives who were forever looking down their Ivy League noses at ordinary working people.

Instead of congratulating themselves for the belated public conversion of House Democrats to the tax-cut school, Republican "populists" showed themselves to be more concerned with abstractions, such as capital formation, than with cutting taxes for American workers. In 1981, when nobody's preferences or loopholes were touched, the tax-cut vote had been ouchless. But in 1985, there was a crunch: lower individual and corporate tax rates were to be financed by the repeal of established preferences. That's when the "populist" Republicans found themselves chanting the mantra of "pro-family" and "pro- growth" and voting "no." All of this was in spite of the fact that the bill's minimum increase for child deductions is 50 percent above the current law, and that George Gilder and Art Laffer, the intellectual co-captains of supply-side, were publicly on record in support of the Democratic bill.

The so-called populist Republicans turned out to be fiscal first cousins of those anti-defense Democrats who insist that they favor some weapons system or another. But never the one that is before Congress in any given year. Have doubts been raised and expressed about such Democrats' commitment to a strong national defense? You bet. Will doubts now be raised and scorn heaped upon the "populist" Republicans? You bet. After all, when was the last time anyone sat down on a stool at the neighborhood tavern and heard the guy next to him ask: What's to be done about capital formation?

In fairness to Jack Kemp, he did become belatedly, in the judgment of the White House, an important player in winning the support of 70 House Republicans for the president's position. But that, while important, was "inside" House politics. Presidential politics is "outside," and there, in the words of a powerful House Democrat who has grown to respect the New Yorker's political skills, "Jack Kemp looked indecisive and uncertain." Kemp, a gifted and creative politician, can recover, but the myth of the anti-elitist, populist Republicans is a permanent casualty of the House fight over the tax bill.