Congressional budget conferees agreed yesterday to a narrowly balanced budget of $613.3 billion for fiscal 1981 that bows so deeply to Senate demands for big defense spending increases that it could collapse in the House.

Nearly half of the House Democratic conferees vowed to fight the package on the House floor next week, and House Budget Committee Chairman Robert N. Giaimo (D-Conn.) said the struggle for passage will be "very difficult."

The House conferees broke a two-day impasse on the guns-versus-butter spending priorities when they voted 10 to 6, over the opposition of five Democrats and one Republican, for a package that includes $153.7 billion for defense -- an increase of $18 billion over what Congress expects to spend for defense this fiscal year.

The compromise was far closer to the Senate proposal of $155.7 billion than the House figure of $147.9 billion, requiring wide-ranging cuts in social programs to accommodate the increases in military outlays within the confines of a balanced budget.

The budget is cushioned by a surplus of $500 million, or less than one-tenth of 1 percent, making it nominally, at least, the first deficitless national spending program in 12 years.

Whether it will stay in balance is another matter, however, if the recession puts as much pressure as some economists and lawmakers fear it will on both revenues and unemployment-related spending obligations.

The budget avoids dipping into President Carter's imperiled oil import fee, as the Senate plan had done, reserving it solely for a possible tax reduction. But it seeks to limit any early tax-cut action to the budget surplus for $500 million. The House had recommended a surplus of $2 billion. s

The domestic spending cuts were spread broadly through the budget, with the conferences's actions mainly affecting transportation programs, fuel assistance for low-income people, subsidized housing, food stamps and productivity-related scientific research, according to one house budget expert.

House proposals would be cut by $1.2 billion for education and jobs, by $850 million for transportation, and by $750 million for food stamps and other income-security programs. Money the Senate added for Saturday mail deliveries and for a modest continuation of revenue-sharing with the states would also be cut.

While Giaimo described it "as the best deal we can get;" five other moderate-to-liberal House Democrats -- William M. Brodhead (Mich.), Richard A. Gephardt (Mo.), Norman Y. Mineta (Calif.), Timothy E. Wirth (Colo.) and Leon E. Danetta (Calif.) -- said it was too heavily weighted toward defense at the expense of social programs and a comfortable surplus.

"Now it all depends on the Republican votes," said Gephardt, and most other budget stategists agreed, noting that Gephardt and his allies could cut deeply into moderate as well as liberal Democratic ranks.

Republicans normally oppose Democratic-drafted budget resolutions in the House, and the GOP produced only 22 votes for the initial House budget plan, considerably fewer than had been anticipated.

However, Rep. Delbert Latta (R-Ohio), ranking minority member of the House Budget Committee, said he thought the Republicans could deliver enough votes to get the budget resolution through the House.

Widespread predictions of trouble for the budget resolution in the House came despite a 338-to-62 House vote yesterday to authorize $6.2 billion more in weapons spending than President Carter had sought for next year, indicating a pro-defense mood that the budget resolution's backers are counting on to offset the opposition.

Prospects for Senate passage look brighter. Senate Budget Committee Chairman Ernest F. Hollings (D-S.C.) said the budget plan has "all the characteristics of what the Senate will want," including higher pay for military personnel.

The budget resolution -- first step in the process by which Congress sets targets for spending and then attempts to live up to them -- is expected to go to the House floor next week.

The conferees plan to meet today in an attempt to wrap up the package, including so-called "reconciliation" orders to committees to cut existing spending plans that threaten the budget's balance.

The House has rejected budget resolutions in the past, sending them back to conference for further work. But rejection this year could seriously strain the already heavily burdened budget-control process and further complicate President Carter's and congressional leaders' crusade for a balanced budget to help fight inflation.

A redrawn budget resolution to accommodate House objections could also run into trouble in the Senate, according to Sen. Pete V. Domenici (R-N.M.) a Senate conferee who accused the dissident House Democrats of "trying to destroy the [budget] process" by opposing a compromise that they helped shape.

The conferees also approved final spending figures for fiscal 1980, including a $46.55 billion deficit that is nearly double what was anticipated when the first budget resolution for 1980 was approved a year ago. The new spending total for 1980 is $572.25 billion.