Eulogies for the balanced budget were barely over yesterday before the Senate Budget Committee voted tentatively to add $5.6 billion for the Pentagon to the already defense-heavy spending plan for fiscal 1981.

Overriding objections from some liberal Democrats and conservative Republicans, the committee voted 6 to 5 to raise defense spending to accommodate costs tht have risen because of inflation and other economic pressures since the balanced budget plan was adopted two months ago.

The decision, unless modified later, would raise defense spending to $159.3 billion for 1981 -- $23.6 billion more than Congress sanctioned for defense in 1980 and $13.1 billion more than President Carter recommended in January formilitary spending in 1981.

Although by a narrow margin, the Senate Budget Committee indicated that it will resist cuts in projected defense spending as it seeks to contain the mushrooming deficit caused by the recession.

This could mean either a huge deficit or further cutbacks in social programs. The $613.6 billion budget plan that Congress adopted in June already cut into domestic social welfare programs to provide a big defense spending increae within the confines of a revenue and spending balance.

Both the Carter administration and the Congressional Budget Office have estimated that the recession, by reducing revenues and adding to unemployment costs, will turn the $200 million surplus that was anticipated in June into a deficit of about $30 billion.

With the tax cut that is widely expected to be approved during fiscal 1981, the deficit would go even higher, possibly in the range of $50 billion to $60 billion.

Although an advocate of a strong defense posture, Sen. Henry L. Bellmon (R-Okla.), ranking Republican on the Budget Committee argued in vain yesterday that any attempt to hold down the defict had to begin with holding the line on military spending.

"It seems to me if we're going to hold the line and stay somewhere close to balance," Bellmon said, "we've got to start with defense." But Budget Committe Chairman Ernest F. Hollings (D-S.C.) prevailed with the argument that the extra costs are needed simply to cover programs that the committee -- and Congress -- sanctioned in approving the first budget resolution.

Bellmon's attempt to hold defense spending to the $153.7 billion figure that had been approved in June was rejected 7 to 4. The committee then voted 6 to 5 to go along with Hollings' new recommendation of $159.3 billion.

The extra $5.6 billion the committee approved was $1.8 billion more than the administration's re-estimate of costs for defense programs and $1.2 billion more than CBO's recalculation.

Budget Committee staff members said the money ws needed both to accommodate pay increases recommended by the administration and to keep inflation from eating away at military projects that were approved as part of the first budget resolution.

They said the administration and CBOrecalculations for defense stemmed largely from a faster-than-anticipated rate of spending for already authorized defense projections, incurred in part because contractors were demanding quicker payment to avoid high interest rates for money they borrowed for the projects.

However, Bellmon argued that the committee should stick with its earlier dollar figures rather than trying to expand them to cover the rising costs of specific projects. "Just because General Motors is delivering its tanks faster, it doesn't mean we have to take them faster," he added in elaborating on his position to a reporter.

The committee suspended work last night before reaching the major school programs that have been hit hardest by the recession and before coming to grips with an antirecession jobs package that may be proposed by liberal Democrats on the committee.

On other points in the budget, the committee approved funds for filling the Strategic Petroleum Reserve and to accommodate the administration's proposed 7.8 percent pay increase for federal workers. A 6.2 percent pay increase had beer anticipated in the first budget resolution.

Meanwhile, in the House, Democratic leaders failed again yesterday in an attempt to resolve a dispute over a $10 billion package of spending cuts and revenue measures that is holding up House action on the second budget resolution.

The House Rules Committee put off action on the package for a second time this month when it became clear that there were not enough votes on the committee to restrict amendments when the package reaches the House floor. t

Budget leaders fear that this would open the package -- originally designed to keep the budget at or near balance -- to an amendment free-for-all and thereby doom it.

House Speaker Thomas PL (Tip) O'Neill Jr. (D-Mass). met later with Rules Committee Chairman RICHARD boiling (D-Mo.) and Budget Committee Chairman Robert N. Giaimo (D-Conn.) in an attempt to chart away out of the impasse. But Bolling and Giaimo said afterward that the meeting didn't solve anything.