Administration officials and liberal Democrats who thought Federal Reserve Board Chairman G. William Miller would push for lower interest rates in return for a smaller tax cut are likely to be severely disappointed in the months ahead.

For unless the inflation rate should take a sudden nosedive (an improbable eventuality), the nation's central bank is unlikely to change the course of action it has pursued since April: making money more expensive to discourage spending by businesses and consumers.

When Miller, the former Textron Corp. Chief executive who has headed the Fed since March, signed off on the president's decision to reduce his tax cut package from $25 to $15 billion for fiscal 1979, many believed he and the president had an unspoken understanding. To wit: That Miller, who now will have $10 billion less in budget deficits to worry about, could ease up on the monetary purse strings.

There was no such agreement, no quid pro quo, either "fprmal or informal, implicit or explicit," Miller said recently.

"A lot of people around here who think that interest rates rises will choke off the recovery might have read something into tax cut changes," said one administration economist. "There are a lot of people around here who th"There are a lot of people who assume some kind of bargain was struck that the Fed would not tighten any further and might even ease up some."

If so, said another administration official, they will be disappointed. "Anyone who knows anything about the Fed knows that one guy cannot deliver the Fed. Miller's got a bunch of hawks there. The chairman, especially a new one, has only one vote."

Liberals, who hailed the appointment of Miller to succeed Arthur Burns, had been severely disappointed with Miller's early performance as Fed chairman. His public proclamations about the evils of inflation and the need to combat it out-Burnsed Burns, many felt. When Miller began to call for a $15 billion tax cut, rather than the $25 billion Carter originally proposed, and the president followed his advice, their hopes were revived.

It was as deep an involvement as the usually aloof Fed has had in years in the formulation of domestic economic policy. Miller praised the president's action as resulting in a "better balance" of monetary and fiscal policies.

But Miller scotched the nation that the Fed will necessarily ease up on the climb in interest rates to hold down the growth of checking accounts and currency in circulation.

The change in tax policy "obviously decreases the pressure" the federal deficit will put on monetary policy in the fourth quarter of the year, Miller said in a recent interview. "But no one can predict the conditions that will exist then. No one knows what extraordinary events may occur."

But, Miller is quick to add, "Whatever the conditions are (toward the end of the year), the pressures will be less than they otherwise would have been. I call it the 'delta effect' - a reduction in whatever we might have had to do."

The chairman, who has settled into his role as central banker more authoritatively and quickly than most observers expected, also argued that he had no special input in the president's decision.

"I was asked by the press what my recommendations would be and I told them. I did not tell the president anything different than I had already said publicly," Miller asserted.

Miller said he hoped that interest rates would be lower at the end of the year, but there are any number of pitfalls, including the rate of inflation; the possibility of anticipatory hiring, buying or pricing; the international state of the dollar; and the energy situation.

Henry Kaufman, the respected chief economists of the investment banking firm of Salomon Brothers, doubts that economic conditions over the next several months will permit the "dovetailing" of monetary and spending policies that the administration is hoping for: easier monetary policy and more stringent fiscal policy.

"We need a significant slowing on the fiscal side to quickly slow the rate of inflation.Such a slowing, if it comes at all, could be belated," Kaufman said.

Last Thursday's report that the money supply surged $4.2 billion will make it even harder for the Fed to keep from tightening monetary policy again soon unless the jump is followed quickly by reductions in the amount of checking accounts and currency outstanding.

When inflation begins to accelerate, the Fed tries to "lean against" it by reducing the amount of dollars in circulation to buy goods and services. It does that by raising interest rates through its open market operations. Many administration economists do not think that the current inflation is coused by excess demand, but rather by businesses and workers trying futilely to catch up with the purchasing power they lost in the big inflation caused by oil price increased in 1973 and 1974.

Federal Reserve economists and Miller believe that the economy is much closer to full employment and excess demand than do most of Carter's advisers.

If anything, thew prospect is for higher, rather than lower, interest rates, Kaufman said. "We have a 7.5 percent federal funds rate now. It could be 8.5 percent by the end of the year. Triple-A corporate bonds are now about 9 percent. They could be 9.5 percent to 10 percent," he said.

The higher rates are not likely to kill the pickup in investment spending that the government says is necessary to keep the recovery going through the latter part of 1978 and 1979. But surveys by the government and by private economists give conflicting information about how much businessmen plan to invest in the coming year.

But the higher rates are likely to make mortgages even harder to come by, as depositors in savings and loan associations take their money out of S&Ls and put their funds instead in high-interest market securities such as Treasury bills.

Furthermore, as Continental Illinois Bank and Trust Co. noted, besides the Fed's desire to restrain inflation, there is a strong demand for credit from businesses. Increased demand for borrowings puts upward pressure on interest rates as well.

"In short," said one observer, despite the president's reduction in the tax package and Miller's approval of the move, "interest rates appear to be headed higher, not lower, for the balance of the year."