The House adopted a $631.7 billion federal budget for fiscal 1981 yesterday after rejecting a Republican attempt to give President-elect Ronald Reagan an updated version of the impoundment authority that Congress took away from President Nixon in 1974.

The Republicans arguing that Congress cannot control itself on spending, wanted Reagan empowered to refuse to spend any money in excess of the congressional spending ceiling.

The House approved its version of the budget on a basically party-line vote, 203 to 191, as the Senate worked toward passage of a somewhat different spending plan totaling $633 billion.

Republicans wanted to delay the budget until they take over the White House and the Senate in January. But Deomocratic leaders in both houses were pushing for final approval in the current lame-duck session of the 96th Congress. Congress was supposed to enact the budget before the start of the fiscal year Oct. 1, but put off action until after the elections.

Both houses, forced by the recession to abandon plans for a balanced budget for the first time in 12 years, anticipate a deficit for the 1981 fiscal year, which began Oct. 1.

The House-approved budget forecasts a $25 billion deficit, even including the 2 percent cut in domestic spending that Reagan promised in his campaign and House Democrats gleefully incorporated into their budget proposal.

The Senate Budget Committee's proposal includes a $17.9 billion deficit, and yesterday the Senate voted 72-to-18 against a proposal by Sen. William Proxmire (D-Wis.) to make enough cuts -- $21.9 billion altogether -- to bring the budget into balance this year.

While action in the Senate focused on both Democratic and Republican proposals for spending cuts, the only debate in the House was over the Republican effort to enhance presidential powers to curtail spending.

"Don't turn back history. Remember the impoundment fights in the days of Richard Nixon," declared House Budget Committee Chairman Robert N. Giaimo (D-Conn.) in fending off the GOP effort, which failed on a basically party-line vote of 154 to 232.

Republicans had wanted to include broad presidential impounding power in the budget resolution but were blocked by the House Rules Committee on parliamentary grounds. So they tried to get the House to approve a "sense of the 96th Congress" statement to the effect that Congress would subsequently empower Reagan to "reserve" any federal expenditures that exceed the congressional budget ceiling through the end of the fiscal year, on Sept. 30, 1981. They said that Reagan would have to apply such cutbacks "equitably in order to retain the important spending priorities adopted by Congress."

Republicans contended that the proposal was nowhere near as far-reaching as the pre-1974 impoundment authority, under which Nixon infuriated Congress by refusing to spend up to $20 billion a year that it had appropriated for domestic projects.

"Until we get our house in order, we have no choice but to give the president the power to do what the Congress cannot do or has not done," argued Rep. Delbert L. Latta (R-Ohio), ranking minority member of the Budget Committee and leader of the Republican effort on the floor.

But the Democrats insisted that it was a "backdoor return to impoundment" amounting to congressinal default of its responsibilities for fiscal restraint and establishment of fiscal priorities.

It was Nixon's excessive use of impoundment, Giaimo reminded the House, that prompted the 1974 congressional budget act, which ended presidential impoundment and set up the congressional budget process.

"This Congress is not ready to give up its powers and duties . . . to say it's powerless to control spending," argued Giaimo.

For defense-minded conservatives, Giaimo offered another reason for voting against the Republican proposal. Because most domestic spending is locked in by entitlement and other legally required programs, defense spending would be the likeliest target for presidential cuts, he warned.

While rejecting the Republican impoundment proposal, House Democrats went along with a GOP proposal to require that Congress pass a so-called "reconciliation" package of up to $10 billion in budget savings before adjourning on Dec. 5. The package of spending cuts and revenue-raising measures is currently in a House-Senate conference.

The House-approved budget includes $5.4 billion to accommodate a tax cut of roughly $30 billion to take effect July 1, 1981. The resolution now before the Senate includes no provision for a tax cut, although Senate Budget Committee Chairman Ernest F. Hollings (D-S.C.) said yesterday Congress could make allowance for it in the budget when it considers tax cut legislation next year.

The House budget of $631.7 billion amounts to $41.4 billion more than Congress approved for the 1980 fiscal year. It contemplated deficit of $25 billion is less than half the $59 billion deficit for 1980. Its biggest area of increase is defense spending, which would rise from $135.7 billion in 1980 to $158.7 billion in 1981, an increase of 17 percent compared to the overall budget increase of 7 percent.

The Senate is expected to complete action on its budget proposal today, and congressional leaders hope their differences can be resolved in conference within a few days.

Among Washington area House members, Reps. Joseph L. Fisher (D-Va.) and Herbert E. Harris (D-Va.) and Rep. Michael D. Barnes (D-Md.) voted against the Republican impoundment proposal, while Rep. Robert E. Bauman (R-Md.) voted for it. On passage of the budget resolution, Fisher, Harris and Barnes voted for it, while Bauman and Rep. Marjorie Holt (R-Md.) voted against it. Holt was not recorded on the impoundment vote.