ITS LUDICROUS, but not astonishing: In the final stage of enacting the federal budget, Congress has fallen into a deadlock over public works. Everything else has been negotiable - taxes, defense, pensions, all the large and genuinely hard questions. But not public works. The House wants to push into the budget another $1 billion for construction and fix-up, to reduce unemployment. That, after all, is the conventional and accepted thing to do in an election year. The Senate thinks that it's bad policy and a waste of money. The Senate, of course, is correct.

Since a Senate-House conference on the budget resolution has not been able to resolve this interesting philosophical dispute, the chairman of the Senate Budget Committee, Edmund Muskie (D-Maine), finally went back to the Senate floor on Thursday afternoon and asked for a vote of instruction. At that point the Carter administration stepped up its vigorous lobbying campaign, led by Vice President Mondale. And which side do you suppose it was lobbying for?

The Carter administration is deeply concerned about the rising rate of inflation. It is filling Washington with warnings of the ferocious rigor that it will apply to the 1980 budget. But it's the 1979 budget that now confronts Congress and on that one, the administration on Thursday was urging senators to add the extra billion dollars for public works that most of them consider unnecessary. It is another example of the fashion in which President Carter's White House keeps undercutting its own strategy on inflation. The exhortations about the need for stringency are repeatedly followed by special exceptions, like this one, to meet prior commitments or the heartfelt pleas of old friends.

The administration wants the public-works money because it is part of Mr. Carter's urban policy, as he announced it last March. Congress has not been terribly enthusiastic about the urban policy. The White House evidently fears that, if the public works are dropped, the whole program will vanish, like the Cheshire Cat, leaving nothing but the smile.

But public construction is always an inefficient way to create new jobs - particularly in the inner city. It provides too many of the jobs in the wrong places, for people who don't need them. Sen. Muskie argues that the present proposal would cost $71,000 per year every job that it created for disadvantaged people. In contrast, the federally subsidized jobs under CETA - the Comprehensive Employment and Training Act - cost only $9,200 a year. Mr. Muskie and the Budget Committee's ranking Republican, Henry Bellmon of Oklahoma, joined in denouncing the billion-dollar public-works provision as "unacceptably expensive, inflationary and duplicative of existing programs."

When they put the question to the Senate on Thursday, it voted 63 to 21 against the public-works money. That was a defeat for the administration, but a victory for the administration's anti-inflation drive. Will the two houses now reach a settlement and pass a final budget resolution next week? We hope so, since the fiscal year begins on Oct. 1.

Until a few years ago, there was only one federal budget - the one that a president announced every January. But the reform act of four years ago changed things fundamentally. It is now Congress that has the last word, and this year offers a particularly clear example. As Mr. Carter presented it last winter, the budget was to have a deficit of $60.6 billion. As Congress is now about to enact it, the deficit will be held to about $39 billion. Of the two, it is the congressional version that will have the force of law. That's why it is worth paying attention over the next few days to the final form of the budget resolution - public works and all.