The Reagan administration went to Capitol Hill today to argue against a tax cut that would stimulate private enterprise; to keep tax revenue for the federal government at the expense of the states, and to keep the government squarely on the backs of the people.

This stance may not sound much like Reaganomics in action, but the issue in question, withholding tax from gambling winnings at the track, never has been one to foster rational or consistent arguments.

Members of Congress have introduced a number of bills to repeal or modify the 20 percent withholding tax on payoffs that return more than $1,000 at odds of 300 to 1 or more. One proposal would raise the threshhold for the withholding tax to $5,000. Another, sponsored by Rep. Ken Holland (D-S.C.), would allow gambling losses to be carried forward or backward from one tax year to another, thus eliminating one of the most crushing inequities that gamblers face.

Representatives of the racing industry appeared before the subcommittee on select revenue measure to advocate the elimination of the tax, most of them citing the same basic financial argument.

"Every dollar at a race track is wagered and rewagered an average of 3.5 times," said Bob Mulcahy, executive director of the New Jersey Sports and Exhibition Authority, which operates the Meadowlands Race Track. "This is due to the return of 81 percent of the dollars bet on an event and the subsequent rebetting of these dollars. The effect called turnover or churn means that the $5 million withheld from patrons (at the Meadowlands in one year) which cannot be bet later translates into $17.5 million in reduced wagering.

"The withholding at the Meadowlands," Mulcahy concluded, "costs the state of New Jersey, its sports authority and the racing industry $3.5 million a year."

Nationally, the Internal Revenue Service withholds $71 million a year. A study by the American Horse Council indicates that the pay-as-you-play policy nets $17 million in revenue more than the old system that required bettors to fill out an IRS information form before collecting. But taking $71 million out of circulation costs the tracks about $250 million in handle, which would have yielded about $50 million in revenue and state taxes.

If ever there were a textbook illustration of supply-side economics at work, this is it. Reagan's theorists have argued ceaselessly that a reduction in taxes will stimulate business activity and ultimately work to everyone's economic benefit. But in one little microcosm where this thesis can be documented, the administration opposes the tax cut.

John E. Chapoton, assistant secretary for tax policy at the Treasury Department, represented the administration and defended the tax. He maintained that withholding is "directed at . . . unique and occasional windfalls--the cases in which it is reasonable to expect a taxpayer to have net gambling winnings for the year." Chapoton ought to have the experience of going $2,000 into the hole on an afternoon at Pimlico, bailing out partially by hitting a $1,500 triple in the ninth race, and having $300 of his "profits" withheld.

An argument that Chapoton could not make, however, is the one that the Treasury Department put forth in 1976 when it originally advocated the withholding tax. Then the tax was seen as a source of potentially great revenue.

"This tax generates relatively tiny revenues for the federal government," Churchill Downs President Lynn Stone told the subcommittee. "It is a far cry from the $500 million figure projected by Treasury . . . in 1976."

Even Chapoton could no longer argue this point. "The withholding on gambling losses is not a major revenue matter," he acknowledged.

Then why keep it?

"It is a compliance issue," he said.

In other words, even if the tax has no economic rationale, it is a way to keep the government on the backs of America's horseplayers.