Last August the Reagan administration confidently predicted that the federal budget deficit would fall to $172 billion in fiscal 1986. Now, less than four months later, the president and his aides are scrambling to cut next year's spending by more than $42 billion to hold the red ink to that level. The budget-makers are once again running ever faster just to stand still.

The deficit estimates have risen, as usual, for a variety of reasons:

* Slower economic growth in the second half of this year, which means a lower gross national product in fiscal 1986 and therefore a lower level of tax receipts.

* Added spending for a number of programs, including farm price supports, and failure by Congress to agree to cut some programs as the administration had proposed.

* Higher interest payments on the national debt, which will be nearly $40 billion bigger at the end of fiscal 1985 than estimated because this year's deficit has gone up by that amount.

Meanwhile, the earlier claims that rapid economic growth would allow the nation to grow out of the deficit dilemma have fallen by the wayside. President Reagan has accepted the unanimous view of his top advisers that he should not base budget policy on such a long-shot possibility.

At the moment, the economy is adding to the administration's budget headache. The abrupt slowdown in economic growth that hit about midyear is hurting revenues. Should the economy not pick up soon, tax receipts will fall ever further below what the Treasury Department has been counting on.

Treasury Secretary Donald T. Regan said last week that receipts likely will be about $14 billion lower than expected this year as a result of the slow growth in the third and fourth quarters of 1984, even if faster growth resumes in the first quarter of 1985.

In the longer term, the administration is assuming that the economy will perform extremely well and that no recessions will intervene. Any bad economic news in the next few years would throw the budget estimates off track, just as it is doing now.

The administration assumes that the economy will expand about 4 percent faster than inflation, at least through fiscal 1988. That would reduce unemployment to below 6 percent.

Meanwhile, inflation is projected to decline to a 3.5 percent rate. The Treasury is expected to be able to borrow short-term money for about 5 percent and long-term money for less than 6 percent, compared with today's levels of 8.7 percent and 11.7 percent, respectively.

Lower tax receipts for fiscal 1985 and 1986 because of the economy are only part of the story. Congress, with President Reagan's approval, added several billion dollars to this year's spending level -- compared to the administration's August figures -- before quitting for the election. Other programs that were not changed, such as farm price supports, are also likely to cost billions more. Low market prices and big crops are expected to push the cost of price supports to more than $14 billion, about $3 billion more than the August estimate.

An unintended side effect of this year's tax bill, also passed with presidential approval as a "down payment" on deficit reduction, is costing the government an unexpected $14 billion. The bill called into question the tax-exempt status of some promissory notes issued by local housing authorities under a guarantee from the Department of Housing and Urban Development. Now HUD is having to spend money to replace the the guarantees since new tax exempt notes cannot be issued.

Altogether, spending for the current 1985 fiscal year, which is in its third month, is estimated by the Office of Management and Budget to be headed for about $968 billion, up about $38 billion from the August figure. At the same time, the revenue estimates are being eroded by the slower economy.

This combination of more spending and less-than-expected revenues has caused OMB to increase the projected size of the 1985 deficit from $172 billion in August to about $210 billion.

Some congressional budget experts say they think that the latest OMB estimates for 1985 spending are as much as $15 billion too high. About half of that difference is due to an assumption that the Defense Department will, like last year, be unable to spend the money allocated to it.

The administration also is assuming a resumption of rapid growth in Medicare outlays rather than a continuation of the more modest 1984 rate of increase, with the difference worth another $3 billion or $4 billion.

However, the congressional budget experts also say that administration revenue figures are probably $5 billion or $6 billion too high. They say they think the deficit will be closer to $200 billion than the administration's $210 billion.

The United States is already borrowing more than $1 for every $5 it spends, so a bigger dose of red ink in 1985 just makes the problems worse, as President Reagan acknowledged in his news conference last week.

On that occasion, when asked why the deficit estimates have risen so much since the election, Reagan replied, "Well, some of the same things, including every year that you continue deficit spending you add that much more to the debt and that much more interest that has to be paid, a very sizable increase in that. So that's just one of the factors."

The estimate for this year's net interest on the publicly held portion of the national debt has risen from $130 billion in August to $133 billion. With the deficit now about $38 billion higher for 1985, that means that in 1986 the debt will be $38 billion higher than it otherwise would have been. Just like any individual or business that incurs more debt, the government is going to have a bigger interest bill.

If the government begins fiscal 1986 with a $38 billion larger debt than it had planned, and the interest rate is, say, 10 percent, interest payments will have to be nearly $4 billion higher.

The total increase in the debt this year likely will be in the neighborhood of $225 billion, once borrowing for spending not included in the budget is included. That is why the interest bill in 1986 is now expected to be about $154 billion, up from $133 billion this year.

The rise in the level of interest payments in 1986, therefore, accounts for about $8 billion, or one-fifth of the $40 billion spending increase the president is trying to offset by slashing or eliminating a host of programs.

Meanwhile, the revenue estimates remain a major question. What matters most for revenues, as OMB pointed out in its August budget review, is how much the current-dollar gross national product rises rather than how much inflation-adjusted GNP rises.

Usually, discussion about economic growth centers on the latter, so-called real GNP. That is the measure that, after rising at a seasonally adjusted annual rate of 10.1 percent in the first quarter and a 7.1 percent rate in the second, dropped off to a weak 1.9 percent rate in the third. This quarter, most forecasters expect it to do no better -- and perhaps worse.

Taxes are levied on current incomes, whatever may be happening over time to the purchasing power of the dollars being received. That means that for revenue-estimating, current-dollar GNP is the experts' starting point; and on that front, the outlook has deteriorated.

The Reagan administration's economic assumptions behind the August budget numbers called for an 8.9 percent increase in current-dollar GNP in calendar year 1985, compared to this year's level, and an 8.6 percent rise in 1986. However, even if the economy gets back on a 4 percent real-GNP growth track early next year, the 1985 level of current-dollar GNP probably would still be no more than about 7.5 percent higher than in 1984.

The roughly 1.5 percentage-point difference between the August growth estimate and the current one could easily knock off a comparable chunk of receipts.

At his news conference, the president noted succinctly: "Growth improves revenues."

Less growth in this case means more running in place to stay even.