The Reagan administration has begun work on the 1984 budget with some internal projections suggesting the deficit could be nearly $175 billion in that fiscal year if there are no further tax increases or spending cuts.

That is far beyond the $84 billion that Congress estimated for 1984 in the budget resolution approved last spring, and would exceed even the $152 billion projected just last month by the Congressional Budget Office. The $175 billion figure is not what President Reagan will propose. Rather, as explained by a White House aide, it is a measure of how large a problem he will face as he works in the next few months to bring the deficit down to acceptable levels.

For political reasons, presidential aides have tried to defer budget talk until after the Nov. 2 election. And none of the major shaping decisions has yet been made; the budget, which is for the year beginning next Oct. 1, does not have to be sent to Congress until early next year.

The deficit estimates are starting points for the budget process; they are guesses as to what the deficit would be without any changes in current policy or law.

They assume Reagan will not flinch from his presently planned defense buildup; he has indicated as much, even though Congress, in the spring budget resolution, called for some curtailment.

They also are based on the assumption that there will be no tax increase. On the contrary, they assume that the sizable tax cuts already voted by Congress for 1983 and beyond will be allowed to take effect as planned. The largest of these involves the so-called indexation of the individual income tax beginning in 1985 to offset the tax effects of inflation. Without indexation, many people automatically move into higher tax brackets each year as their incomes rise.

The president, who was raked by conservatives for supporting this year's tax increase, was asked at his news conference last month whether he would "flatly rule out any tax increases" in 1984. "Unless there's a palace coup and I'm overtaken or overthrown, no, I don't see the necessity for that," he answered.

The deficit estimates further assume that the economy will not improve dramatically by fiscal 1984, but will stay on the slow-growth path the administration itself has officially projected. Last year an optimistic economic forecast helped the president bring down the projected deficit at budget time. This year he has a new chairman of the Council of Economic Advisers, Martin S. Feldstein, who is already on record as foreseeing only slow-to-moderate growth, and who is regarded as most unlikely to let his forecast be altered for political purposes.

The deficit estimates assume, finally, that there will be no cuts in domestic spending programs beyond those already voted by Congress last year and this--but the president has indicated that he will propose additional cuts in this sector to reduce the deficit.

In a sense, the new estimates are thus a measure of how large a further burden domestic programs must bear if Reagan sticks to his guns on defense spending and taxes.

"Without a tax increase, and keeping programs at the levels in current law, I don't see how we can keep the deficit below $180 billion in 1984," said a senior congressional budget analyst. "It will be almost impossible."

"What is this president going to put on the table?" he wondered.

Reagan, in saying last month he saw no need to increase taxes, said he would propose "more reductions in government spending."

The CBO, for its part, said last month that "substantial spending reductions will require changes in areas of the budget that have thus far been excluded from major spending cuts--defense and pensions, especially Social Security."

Reagan seems unlikely to retreat much from his proposed five-year $1.6 trillion defense build-up. Only a few months ago he touched off a small storm on Capitol Hill by saying he would not be bound by the defense spending limits contained in the congressional budget resolution for 1984 and 1985.

Reagan also has firmly refused to eliminate the final 10 percent installment of his across-the-board individual income tax rate cuts, scheduled for next July 1.

Social Security, the largest of all domestic spending programs, will be an obvious cost-cutting target for Reagan and Congress after the elections, when a presidential task force is scheduled to recommend ways to reduce benefits or otherwise shore up the tottering system. But trimming current benefits is a politically risky course that neither Reagan nor Congress may be willing to take. Instead, they may decide to move against only future benefits, which would mean little cost-cutting in 1984.

As to other domestic programs, administration planners have spoken hopefully of finding some way to restrain runaway Medicare costs, which are outpacing the inflation rate. But there is doubt on Capitol Hill whether the deficit now envisioned for 1984 can be brought down to size with cuts in Medicare and other entitlement programs alone.

The Office of Management and Budget has already begun the process that will culminate in the budget Reagan will send to Congress early next year, but the major decisions have been put off until after the election, said OMB spokesman Edwin L. Dale Jr.

The key factor in any 1984 budget outlook is the performance of the economy. If it expands rapidly, the deficit will fall below expectations; if it continues to stagnate or recovers only modestly, the deficit will rise. This is partly because slow economic growth means smaller incomes, lower profits, and thus less tax revenue for the government. It can also mean less inflation, which also can mean less money for the tax collector.

Likewise, a recessionary economy and high unemployment rates increase federal outlays for social programs. The 1984 economic forecast has not yet been made. Previous administration forecasts have been criticized as too optimistic.

Even last summer, top administration officials were keeping their distance from the official forecast of 4.4 percent growth in 1983. The CBO's latest projections are based on the economy expanding at 3.6 percent in 1983 and 3.7 percent in 1984. These estimates are more pessimistic than what the CBO and the administration had projected last winter. Many private and congressional economists think the economy will expand even slower.

According to the CBO, each one percent falloff in growth per year adds $10 billion to the 1983 deficit and $28 billion to the 1984 deficit. "It really wouldn't be very hard to exceed our $152 billion deficit projection if the economy is more sluggish," said one CBO analyst.

There are other factors that may drive deficits upward. High crop production will depress farm prices for corn, wheat and soybeans, thus increasing government outlays for crop storage and support payments.

The senior congressional budget analyst also points out that many weapons systems started in 1983 will blossom into larger military outlays in 1984 and 1985. "A lot of defense outlays will really be on board by then," he said. "The horse is really out of the barn."

Finally, pressures created by rising military and entitlement programs will further squeeze other areas of government. "Everything else in the budget will have to stand still," the analyst added. Given all the areas Reagan has already put off limits, saying there will be no tax increase and no slackening in the defense build-up, "I don't see any way out," he added.