President Carter yesterday sent Congress a $739.3 billion budget for 1982 in which -- in contrast to the plans of President-elect Ronald Reagan -- domestic spending would not be deeply cut and taxes would rise.

"We cannot do all that we wish at the same time," Carter said in defending these choices in his final budget message. "But we must provide for our security, establish the basis for a strong economy, protect the disadvantaged, build human and physical capital for the future, and safeguard this nation's magnificent environment."

The president said he was not recommending large tax cuts or economy-boosting spending increases, except in defense and energy, "because persistent inflationary pressures dictate a restrained fiscal policy." Instead, Carter proposed more tax increases than tax cuts for both 1981 and 1982, using the proceeds to help reduce the 1982 deficit to $27.5 billion to help combat inflation.

David A. Stockman, Reagan's choice for director of the Office of Management and Budget, immediately denounced Carter's budget as a "very political document," adding, "We think we are going to have to revise it from top to bottom."

The incoming OMB director said Congress had already rejected the tax increases Carter proposed, and that if they are dropped, a better estimate of the 1982 deficit would be $50 billion. Stockman promised Reagan would propose major tax and spending cuts but said no decision on specific spending reductions have been made.

But Reagan will have to convince many skeptical members of Congress and a host of beneficiaries of a host of government spending programs that they can be cut back so far and still meet essential needs. The Carter administration's budget arguments provide ammunition for those skeptics.

Carter decided first on the spending side of the budget, including $23.2 billion more for defense spending and a drop, after adjustment for inflation, in domestic programs. He proposed about $16 billion worth of retrenchments in food stamps, welfare, federal pay and retirement and unemployment benefits; these programs would still grow but not as much as they would have otherwise. Once the spending decisions were made, there was virtually no room for tax cuts in 1981 or 1982, Treasury Secretary G. William Miller said.

Under the budget, the federal government would spend a total of $739.3 billion for the year beginning Oct. 1, up 11.6 percent from this year's $662.7 billion.

Taxes would rise by more than $100 billion in 1982 with government revenues reaching $711.8 billion. In 1980 the government took in only $520 billion.

The deficit for 1982, $27.5 billion, would be half the $55.2 billion now estimated for this year but would still be the 14th annual red-ink figure in a row. The deficit for 1980 was $59.6 billion.

The Reagan budget changes, based on an entirely different view of the economy, are supposed to be unveiled no later than mid-February as part of a package of exonomic policy proposals intended to reduce inflation and spur economic growth. Reagan is expected to propose at least $50 billion in personal and business tax cuts for fiscal 1982 and reductions in many federal spending programs that probably will top $30 billion.

While Reagan may cut all other federal programs where Carter would not, there is no disagreement on providing for security. Carter proposed spending $184.4 billion for defense in 1982, up from $161.1 billion this year and only $135.9 billion in 1980. Military spending this year is rising a huge 8 percent fastger than inflation and would rise another 5 percent in real terms next year under the Carter budget. These increases are so large it is uncertain Reagan will seek to add to them significantly.

Even with the big jump in defense, spending in the Carter budget would go up only 1 percent after adjustment for inflation. Overall, nondefense outlays would fall by about 0.2 percent in 1982 after dropping 0.9 percent in 1981.

Carter has retained the personal and business tax cuts that were part of the "economic revitalization program" he offered last August, but some on them "have been delayed or phased in over a longer period in recognition of the continued high inflation rate," the president said.

This concern with inflation, and his commitment to increase defense spending, are the foundation on which Carter's budget rests. He has chosen to let the nation's federal tax burden to reach an all-time high, 22.1 percent of the gross national product, in order to keep the economy from growing too fast.

By one measure, the Carter budget would increase overall fiscal restraint on the economy by about $35 billion in 1981 compared to 1980, and by an additional $25 billion in 1982. "The budget shifts very sharply toward restraint between fiscal 1980 and 1982," Charles Schultze, chairman of the Council of Economic Advisers, noted.

Because of that fiscal restraint, and an expected tight monetary policy from the Federal Reserve, the administration officially forecast a small 1.7 percent increase in GNP in calendar 1981. That prediction allows for the likelihood the economy may decline this quarter and grow little if any in the second quarter. Growth at about a 3 1/2 percent annual rate is forecast for the second half of this year and for 1982.

Such a slow recovery from the recession would mean an increase in unemployment from December's 7.4 percent rate. No peak was specified, but the average for the fourth quarter of 1981 was set at 7.7 percent, suggesting a rate close to or above 8 percent by the middle of the year.

At the same time, inflation hardly improves. Consumer prices will rise 12.6 percent this year compared to 12.8 percent last year, while the GNP deflator, a broader measure of price change, will go up 10.4 percent instead of an even 10 percent, according to the forecast. The slight year-to-year increase in the deflator is entirely attributable to a 10-cent-a-gallon gasoline tax Carter proposed to be effective June 1, Schultze said.

The inflation outlook for 1982 is somewhat brighter, with consumer price inflation dropping to 9.6 percent and the GNP deflator advancing only 8.8 percent. The decline would be due to a slower rate of increase in wages assumed to occur, in part, because of continued high unemployment. In the forecast, unemployment is still 7.4 percent in the fourth quarter of 1982.

That Carter chose not to suggest stimulating the economy to try to reduce unemployment more quickly, as was his goal when he took office four years ago, is a measure of how seriously he has come to regard the threat of inflation. As Miller said at a briefing yesterday, "Inflation is a clear and present danger. It is our highest priority."

As a result, Carter proposes only $3.1 billion in tax reductions for fiscal 1981 instead of the $27.5 billion in cuts he suggested last August. The tax cuts for 1982 would amount to only $18.3 billion.

In addition, Carter has proposed a series of tax increases -- including the 10-cent-a-gallon hike in the present 4-cent tax on gasoline, and withholding on interest and dividends -- that would be larger in both 1981 and 1982 than the tax cuts. Congress refused last year to pass either the gasoline tax increase or withholding on interest and dividends after Carter proposed them.

A variety of other smaller tax increases, along with the first $3.5 billion increment of the gasoline tax, would bring in $5.6 billion during the remainder of fiscal 1981. At the same time, the first part of Carter's tax cuts, including introduction of a 40 percent increase in depreciation allowances for business investment, would reduce taxes by $3.1 billion.

Thus, on balance in 1981, Carter would raise taxes by $2.5 billion, in addition to the already large increases in Social Security, crude oil and personal income taxes -- the latter due to inflation pushing individuals into higher tax brackets.

In 1982, the gasoline tax would raise $14.6 billion, the withholding $3.9 billion, and the other taxes $5.1 billion. The tax cuts, on the other hand, including an $8.5 billion income tax credit originally intended to offset much of this year's Social Security tax hike, would amount ot $18.3 billion, or $5.3 billion less than the tax increases. Making the present 10 percent investment tax credit refundable -- allowing businesses to claim it even if they owed no taxes -- would add $3.5 billion to spending next year, since such crdits count as outlays, not tax cuts.

Rep. James Jones (D-Okla.), chairman of the House Budget Committee, called the budget a "very valid document for the new admnistration to work upon." Jones said it is a "very tight budget and mostly a very honest budget" that "throws a challenge to Congress."

Much of that challenge involves Carter's $15.9 billion worth of spending cuts in domestic programs for 1982. Even though they are far less ambitious than those Reagan's new economic team is planning, many of the same beneficiaries and political considerations are involved.

For instance, Carter would "broaden" the comparability calculations used to relate federal pay to that in the private sector that would reduce the raise due in October from 13.5 percent to 9.1 percent for the military and 8.6 percent for civilian employes. That would save $3.5 billion even if Congress decided not to go along with Carter's further proposal to hold the increases to 5.5 percent under the president'ts discretionary authority. Attempts to change the comparability formula have already stirred up a storm of opposition among federal employe unions and their supporters.

Similarly, Carter again advocated giving cost-of-living adjustments to federal retirees only once a year, not twice. Pressure from the retirees convinced Congress last year not to make that change. This time dairy farmers and food stamp recipients and their supporters whose indexing would also be reduced will likely be up in arms, too.

These and othe such cuts will be hard for Congress to swallow as Carter proposed them, much less on the grander scale Reagan has in mind.