President Carter has given the go ahead for another tight budget next January, with a second sharp increase in defense spending combined with little new money for domestic programs.

The new budget, to cover fiscal 1981, which begins a year from October, would be designed to fulfill Carter's pledge to balance the budget and trim the size of government in relation to the overall economy.

Administration officials say there would be no major new spending initiatives, and - barring a serious recession - on tax cut proposals. The health insurance program the president has proposed would not begin unitl fiscal 1983.

Officials said Carter probably will continue to propose sharp increases in defense outlays for the next several years, in part because of a pledge last year to the North Atlantic Treaty Organization to bolster U.S. forces in Europe.

Carter's fiscal 1981 plan is likely to prove ccontroversial among liberal Democrats, who protested last January when the president asked for higher defense spending at the expense of social programs.

Carter tentatively has set a spending ceiling of about $585 billion for fiscal 1981 - a rise of $53 billion, or 10 percent, from the fiscal 1980 target of $532 billion. The deficit would drop to zero, from $23 billion in 1980.

However, the figure would still fall $7 billion to $8 billion short of the spending total needed to continue current programs and policies intact in the face of still relatively rapid inflation.

Aides said that after adjustment for inflation, the fiscal 1981 budget would show "little or no growth" from the previous year's plan. And many key programs would be held below the pace of inflation.

The outline of the new budget was approved by the president in a preliminary review of the fiscal 1981 budget conducted over the past few days. The White House plans to publish more precise estimates in July.

However, the plan to balance the budget is contingent on the economy escaping a serious recession. But private economists increasingly are beginning to believe a recession is likely,tOfficials concede that if the economy does fall into a serious recession, it would boost spending for welfare and jobless benefits and crimp government tax revenues - making it impossible to balance the budget.

Aides said if the economy were to turn sour, Carter might consider a relatively modest tax cut - stay, in the neighborhood of $15 billion or so. However, they insist the administration still is not expecting a recession.

In January, Carter proposed boosting defense spending by 3 percent more than inflation. The White House did not indicate then that it regarded the pledge to NATO as covering more than one year. Yesterday, however, a key aide familiar with the president's position asserted the promise had been "open-ended."

Although Carter's fiscal 1981 budget probably will once again constrain the growth of domestic programs, officials said the cutbacks in key social programs "probably will be less severe" than they were in last January's plan.

However, insiders say Carter still is considering serious cuts in some major programs, including revenue-sharing grants to states and some minor Social Security benefits.

Carter faces a possible challenge from Congress on the Social Security issue next year as some lawmakers seek to avoid steep increases in payroll taxes scheduled for January 1981.

The White House proposed some modest cutbacks in relatively minor Social Security Programs last January, but so far has yet to see any of them enacted. The lawmakers are planning some Social Security action for 1980.

For all of the controversy surrounding Carter's budget proposals last January, the plan has fared well in Congress. The lawmakers last month approved initial tax and spending targets that parallel Carter's plan.

Aides said if Carter's current proposal for fiscal 1981 holds firm, it would reduce the govenment's share of total output to below 21 percent of the gross national product, from 21.3 percent now.

The drop to a zero budget deficit, from an estimated $23 billion in fiscal 1980, would mark one of the sharpest cutbacks in federal stimulus to the economy in recent years. The fiscal 1979 deficit is estimated at $33.4 billion.