Now that the president's tax bill is passed, what is going to happen to interest rates? Reagan's men blandly assure us that they will come down. But those at the Federal Reserve ask: How can interest rates come down if the Reagan administration's vast tax reductions coupled with boosted military outlays continue to create enormous federal deficits?

The bond markets, under great pressure this week, were trying to provide an answer. Their rather basic fear of a credit squeeze was confirmed by Treasury Undersecretary Beryl Sprinkel's announcement that the federal government would have to borrow a staggering $30 billion to $33 billion, just in the fourth quarter.

Lenders are very reluctant to step in at this time," said Fed Vice Chairman Frederick Schultz. "They have been burned and burned for the past 15 years in the bond market." In effect, the markets think interest rates are going up, not down.

In the past several days, bond prices have plunged, and interest rates have soared. Two-year Treasury notes, auctioned July 22, hit an all-time record yield of 15.92 percent, and the Dow Jones Municipal Bond Index touched a peak of 12.25 percent. All other interest rates were at, or on the edge of, records.

What this dismal picture suggests is that the financial markets have no more confidence in the beneficial effecs of the Reagan program, now that it is about to become law, than they had while it was being debated.

Meanwhile, the economy has been brought to a screeching halt by the increasingly tough policy of the Federal Reserve, endorsed by President Reagan, which focuses all attention on crunching the growth of the money supply. This has produced a historic high in "real" interest rates -- that is, the price of money after allowing for inflation.

According to Sprinkel, the Fed must "hang tough" in a single-minded monetarist approach, no matter what happens to interest rates. That places the burden of fighting inflation on the Fed, and frees the administration to pursue "supply-side" economics, which many others consider inflationary.

Fed Chairman Paul A. Volcker and his fellow governors have long been concerned by the dogmatic approach of the Reagan administration, which pushes a purely monetarist philosophy. Schultz, for example, questions "those people who say that the volatility of interest rates doesn't make any difference, that what you ought to do is just stick to a money supply growth target, hold it there, and to heck with how volatile the interest rates are. I think there are a lot of things wrong with that."

So does West German Chancellor Helmut Schmidt, who said recently in Ottawa that real interest rates in his country, triggered by Fed policy, are at "highest levels since Jesus Christ."

Schultz remarked that it is no coincidence that "this latest slide in the bond market followed the passage of the tax curt. If it had been a smaller tax reduction, you wouldn't have had as big a drop."

Schultz reflects the views of almost all his fellow governors when he says, "I'm very concerned about the large credit demands the government is placing on the financial markets. We are going to have to have more budget cuts if this [Reagan program] is going to work." Unless some additional combination of defense spending cuts along with reductions in the "entitlement" porgrams such as Social Security are put into effect, Schultz says bluntly, "Interest rates are going to go higher."

Schultz believes that if the economy weakens, slipping into a mild recession as now seems certain,t here may be a temporary abatement in interest rates, but that around the first of the year, as the stimulative effect of the tax package is felt, "we will see some upward movement in interest rates again, and that would worry me -- it would worry me a lot."

His concern is on two levels. First, the debilitating effects of high interest rates on housing, autos, small business and certain other sectors of the economy, already in evidence, would of course run even deeper. Second, he predicts that the administration "will come under intense political pressure" to reverse course, and go into a reflationary policy.

"Things could be made a lot easier if we moved in the direction of getting that deficit down." Schultz said. "If we don't, then it's going to be impossible to balance the budget any time in the future."

Henry Kaufman, the Wall Street seer who long has been contending that the administration's fiscal policy is inflationary, is completely in accord with Schultz's analysis. After the president's tax-bill victory in Congress. Kaufman said: "So far, dogmatism has asserted itself. But theory and the real world eventually will clash. The question is, 'When will the administration take a detour, and what will it be?'"