With little debate in the Senate and none in the House, Congress approved its long-overdue budget for fiscal 1981 -- a murky, hastily drawn $632.4 billion compromise that gives President-elect Ronald Reagan and the next Congress the final say on taxes and spending for the year.

The budget provides for a $27.4 billion deficit, about halfway between Congress' original goal of a balanced budget and the $59 billion in red ink recorded in fiscal 1980.

The budget also leaves room for a tax cut of about $35 billion during calendar 1981 and, according to House Budget Committee Chairman Robert N. Giaimo (D-Conn.), anticipates $18 billion in spending cuts to be made next year by Reagan and the new Congress.

But there are big gaps and contradictions. Although the budget was the product of a House-Senate conference, the Senate maintained it was saying House spending should be cut, while the House insisted it was postponing the "difficult and painful" chore, in Giaimo's words, until next year.

Moreover, because Congress dallied on the budget until both bodies had passed their own appropriations bills, anticipated spending already exceeds the budget ceiling by $2.5 billion in the Senate and $7.2 billion in the House. Sen. Henry L. Bellmon (R-Okla.), ranking minority member of the Senate Budget Committee, warned that the actual overrun is more like $11.2 billion.

In any case, Republicans, who will take over the Senate in January while increasing their numbers in the House, were already predicting a whole new budget resolution early next year. "This may be a lame-duck session," said Sen. William L. Armstrong (R-Colo.), reflecting the attitude of many congressional Republicans, "but this budget is a turkey."

Despite protracted fights earlier in the year over budget details, the theoretically final budget passed the House in 20 minutes without even a recorded vote. It passed the Senate, 50 to 38, with many Democrats as well as Republicans opposing it.