Congress gave final approval last night to a defense-loaded, nominally balanced $613.6 billion budget for fiscal 1981 that is rapidly being pushed into the red by the nation's deepening recession.

The House voted 205 to 195 to approve the preliminary spending blueprint, narrowly reversing a vote two weeks ago that scuttled a slightly more defense-heavy plan by 101 votes.

The Senate quickly followed suit, voting 61 to 26 in favor of the plan worked out by congressional budget leaders Wednesday -- nearly a month after it was due and more than three months after Congress launched its budget-balancing drive to curb inflation.

The budget resolution, for Congress' guidance, does not require President Carter's signature.

As in the past, despite early hopes for a bipartisan budget in the House, only 10 Republicans joined all but 55 Democrats in approving the budget in the House. The vote in the Senate was more nearly bipartisan. All Washington-area legislators except Reps. Herbert E. Harris (D-Va.) and Robert E. Bauman (R-Md.) and Virginia's two senators voted for the plan.

Although Congress was voting for its first balanced budget in 12 years, its battle against deficits was far from won.

Administration and congressional experts concede that the budget could be at least $15 billion in deficit -- probably more if the unemployment rate continues to climb -- by the time Congress has to consider its presumably final budget numbers in late summer. Meanwhile, it must also try to live within unprecedented self-disciplinary controls aimed at keeping the fragile balance -- officially a paper-thin $200 million surplus -- from tipping.

But for the time being, passage of the first budget resolution relieved pressure that threatened the six-year-old congressional budget process. The impasse triggered a spending freeze that was holding up $15 billion in emergency appropriations for disaster relief, special unemployment assistance and other politically sensitive programs, and there was mounting pressure for relaxation of budget discipline so that the money could be approved.

"It is about the last train that's pulling out of the station," House Majority Leader Jim Wright (D-Tex.) said in plugging for the budget resolution before the House vote. "If we were to fail," he added, "it would present us with some very unpleasant alternatives."

Although it was slightly modified at the end to win over enough liberal Democrats to assure House approval, the budget leaned heavily toward defense spending at the expense of many socal programs. At such, it represents a substantial victory for the defense-minded Senate and for defense boosters in both houses.

The $613.6 billion package includes $153.7 billion for defense, $19 billion more than has been projected for the current fiscal year. Domestic programs such as mass transit, housing and jobs programs were cut to accommodate the defense increase within the confines of a theoretically balanced budget. Overall, the budget calls for a spending increase of nearly $40 billion over the current year which includes a deficit of $47 billion.

While joining in the push for a balanced budget, President Carter opposed the earlier plan the was rejected by the House but reportedly told House members on Wednesday night that he favored the new version, even though it was not much different from the old one.

In brief House debate Rep. David R. Obey (D-Wis.), a leader of Democratic liberals, called the new version "the best we can," while many Republicans said the budget's balance was a sham.

In the Senate, Howell Heflin (D-Ala.) made a last-minute effort to add $20 million to enable the Law Enforcement Assistance Adiministration to keep its grants program alive, which could have kept the budget controversy going a while longer. But the Senate rejected his effort.

The budget resolution is nearly a month overdue. It was held past its May 15 deadline by reluctance on the part of House Democratic liberals to swallow the big increase in defense spending -- and offsetting cuts in social programs to keep the budget in nominal balance -- that the Senate demanded.

The budget plan anticipates an increase of 13 percent in defense spending over projected outlays for 1980. For nondefense spending the increase is just over 5 percent, meaning the actual cut in most social programs when inflation's erosion of the dollar is taken into account.

Initially, the House passed a budget that comtemplated $7.8 billion less in defense spending that the Senate wanted to its own separate version of the resolution. When House-Senate conferees settled on a plan that gave the Senate all but $2 billion of what it wanted for defense, the House rebelled and rejected the conferees' recommendation. But then, after many liberal Democrats drifted away for the evening, the House turned around and voted to stick by the conferees' defense figure of $153.7 billion.

Caught between what House Budget Committee Chairman Robert Giaimo (D-Conn.) called conflicting mandates, the conferees shadowboxed for nearly two weeks in an attempt to reach a compromise that would satisfy House liberals without losing too many big defense spenders in House and Senate.

Senate Budget Committee Chairman Ernest Hollings (D-S.C.) refused to budge on defense outlays. But, with the impasse deepening and starting to jeopardize the congressional budget process, the House Democratic conferees came up with a proposal that Hollings found acceptable.

It left defense outlays untouched at $153.7 billion but cut $800 million off budget authority for long-term military commitments, leaving a total of $170.5 billion, an increase of $26.8 billion, or 18 percent, over this year. o

It shifted the $800 million to the social spending side of the ledger and added $300 million from the projected surplus to outlays for transportation and fuel assistance to low-income families.

This left a theoretical surplus of $200 million -- a minuscule amount compared to more from administration as well as congressional sources. They say the recession is driving up unemployment and other social service costs at such a rate that it will be difficult if not impossible to keep the budget in balance during the year.