In an act that went unnoticed in their big victory last week, House Republicans apparently stripped from the budget bill a Democratic provision to keep the popular Head Start proghram alive past Sept. 30.

The program, which seeks to put disadvantaged pre-school children on the same educational footing as their better-off peers, is a favorite of minority groups and was included by President Reagan in his "safety net" of programs supposedly beyond the budget knife. He has asked that it be continued in fiscal 1982 at $950 million.

The missing Head Start provision was one of several "sleepers" in the GOP budget alternative that are only now turning up as members have time to go through the bill, which was the thickness of a telephone book, had been hastily pasted together and which most members had no chance to read before they voted.

House Democratic and Republican education specialists yesterday said they were triple-checking the text of the bill to see if it contains provisions for the extension, but it seemed clear it is not in the measure, they said.

There was some confusion about why the extension provision was dropped. Some House GOP aides said it may have been only a drafting error, but others said that when the Republicans were drafting their budget alternative, they deliberately left out any extension of the Head Start program, not to kill the program, but to make sure it will be taken up later in a separate bill so structural changes can be considered.

Charles Radcliffe, GOP staff director on the Education and Labor Committee, was unclear about how it was left out, since the aide who handled that section of the so-called Gramm-Latta amendment or GOP alternative is out of the country.But Radcliffe said there is no question Head Start will be continued and "it is everybody's intention that it be funded at an increased level."

Assuming the president likes Head Start as much as he indicated earlier this year, its deletion from the House budget bill could end up giving him problems. It could also conceivably pose obstacles to extension and allow a fight against it by anyone who opposes the program; taken up alone, Head Start would be an isolated target.

If the issue is taken up later in a separate Head Start bill, it could give Democrats considerable leverage to tack on other things that the president doesn't like. One example: continuation of the Community Services Administration, the anti-poverty agency the president wants to kill.

Some House Democratic aides, in fact, are already licking their chops at the prospect. The major vehicle available to continue the program in a separate bill is a measure already reported out by the House Education and Labor Committee. It includes extension not only of Head Start which the Democrats fathered a generation ago and strongly favor, but of other parts of the Economic Opportunity Act including CSA.

There is nothing to prevent the Democrats from trying to add a few provisions the president doesn't like. That could end up in a tug-of-war in which, it is conceivable, the bill could have a hard time getting through Congress. Or the president might have to decide whether to veto a bill containing the Head Start extension he wants plus a batch of other things he doesn't.

If, however, the matter is taken up in the forthcoming House-Senate conference on the budget bill, which is possible because the Senate has included an extension in its version, it might turn out that the maximum potential funding would be only $820 million.

That's the amount the Senate allowed in its version of the bill and some House sources believe that's the maximum that can now be voted under budget rules.