If President Carter agrees to increase defense spending in exchange for Senate approval of the strategic arms limitation treaty, he will face one of three painful choices going into the 1980 presidential campaign:

He could propose further cutbacks in domestic programs, on top of last January's controversial cuts - a move that would anger traditional Democratic constituent groups just before the spring primaries.

He could abandon his pledge to balance the budget by fiscal 1981 and instead accept another large budget deficit - opening the way for Republicans to criticize him as a big spender in the general election the following November, or

He could seek a smaller anti-recession tax cut than the $20 billion in $30 billion reduction that he otherwise might propose - risking a deeper downturn and cutting back some of the payoff from an election-year tax reduction.

The prospects are not inviting, particularly for a president who already is far behind in the polls - and both Carter and his potential rivals are well aware of his dilemma.

But the fact is, whatever the other implications of the SALT fight, it is rapidly becoming a battle over next year's budgetary priorities.

"In many ways, what we're doing up here now is deciding whether Jimmy Carter gets elected," says one veteran Hill observer with an interest in the coming primaries. "The next few weeks' bargaining could be crucial to it all."

The situation marks a significant change even from a few weeks ago when the White House still was predicting with some confidence that Carter could balance the fiscal 1981 budget and might even rack up a small surplus.

The administration's July 12 budget estimates showed the fiscal 1981 budget likely to contain a deficit of only $1.9 billion - essentially a balance - with some officials predicting privately it would turn into a $5 billion surplus.

Moreover, that margin was projected as likely to grow - to a $46.6 billion surplus by fiscal 1982, $63.9 billion by fiscal 1983 and $87.3 billion by fiscal 1984. Such predictions often prove illusory, but they appeared solid enough then.

But that was before the economic outlook worsened, before the president proposed his costly new energy program, before a chorus of senators demanded increased defense spending and before a tax cut became a likelihood rather than a possibility.

Although the defense spending and energy proposals would have their largest impact in later years, they almost certainly would add several billion dollars to the fiscal 1981 budget, at a time the recession is reducing revenues.

In a rough, "worst-case" estimate, budget, analysts figure that if all those developments were to come to pass, they could shatter the projected budget-balance and bring on a $20 billion to $35 billion deficit.

More important, such developments could affect longstanding domestic programs, requiring a new round of cutbacks larger than the $6.9 billion reductions in last January's budget.

Those cuts angered party liberals, but eventually the president prevailed in Congress - partly because the reductions were viewed as a one-time affair.

But the liberals might not be easy to defeat if the fiscal 1981 budget continues, or even intensifies, this pattern, especially during a time of rising unemployment.

The factors threatening the budget posture this coming year include:

RECESSION: The worsening economic downturn affects the budget in two ways: It decreases the income-tax receipts that the government takes in, and it adds to federal spending for unemployment insurance and other items.

Depending upon whose forecast proves accurate, the slump could slash revenues by $5 billion to $10 billion and boost spending by $4 billion to $12 billion. Total tab: $9 billion to $22 billion.

ENERGY: Budget experts say Carter's new energy proposals could add about $750 million to the fiscal '81 spending plan - not an enormous amount but a lot during a period of scrimping.

DEFENSE: If Carter accedes to Senate demands for increased arms spending - as now seems likely if he wants approval of SALT - that would significantly boost outlays, both now and in coming years.

Budget makers say the proposal by Sen. Sam Nunn (D-Ga.) for a 5 percentage-point boost in military spending, over inflation, would increase the defense budget by $8.6 billion in fiscal 1981 and $53.4 billion by 1984.

A TAX CUT: Carter has hinted that if he ultimately decided to propose a tax cut, it probably would be in the $20 billion to $30 billion range - a move that would shatter the balanced budget and ensure a large deficit.

Key administration officials, nervously eyeing each of these prospects, frankly concede that the budget outlook is a potentially serious political threat, but see little real way out of it.

By far the most welcome solution they envision - at least from a political standpoint - would be if Carter were to propose a tax cut. Then, one aide muses, "we could openly forgo budget balance and not risk taking much heat."

Carter officially is skirting the taxcut issue, arguing the outlook still is too blurred to justify moving rapidly toward tax cut. However, many observers expect him to shift when unemployment begins rising sharply.

The rest depends largely on two developments and what the Senate eventually does with Carter's proposed "windfall profits" tax on crude oil.

If the Senate agrees to the House version of the measure, it could ease the situation slightly, at least in fiscal 1981 and beyond. The tax would provide extra revenues in its first few years, helping to offset some new spending.

If the Senate waters down the House-passed bill, however - as now seems more likely - Carter still has one more act to play: He could cut back the size of his energy program and avoid the extra budgetary squeeze.