The House last night moved toward final action on a preliminzon 1979 federal budget that calls for a tuition tax credit, a rollback of Social Security tax increases due to take effect next year and a tax cut $5 billion smaller than President Carter has proposed.

Although Democratic leaders were optimistic that they could muster enough votes to pass the $498 billion budget, which is deficit of nearly $55 billion, they conceded that the vote would be close.

The House, unlike the Senate, has had problems passing its version of the spring budget resolution, a target that serves as a guide to Congress when it considers taxing and spending bills over the summer.

In the past, Republicans tried to force a balanced budget and big tax cuts, and when they failed voted almost a bloc against the final resolution.

This year, the Democratic leadership, with some difficulty, was able to fight off most major challenges to the budget drafted by the House Budget Committe. That budget was carefully designed to please both liberals and most moderate-to-conservative Democrats.

The House defeated attempts to boost the defense budget and narrowly blocked several amendments that would have trimmed overall spending. Spending-cut proposals are attractive this year because many members are concerned about signaling the country that Congress is worried about inflation, federal spending and large budget deficits. Only heavy, last-minute arm-twisting by House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass) on Tuesday saved the leadership position on an amendment by Rep. Joseph L. Fisher (D-Va.) that would have cut spending by 2 percent across the board. The amendment was defeated 203 to 195.

Had it passed, according to Budget Committe Chairman Robert N. Giaimo (D-Conn.), the target resolution would surely have been defeated because the amendment's impact would have fallen disproportonately on defense spending and on programs such as Medicare and Medicaid.

The Republicans who voted with Fisher would still have been likely to vote against the overall resolution because of the deficit and many liberals would have deserted because of the cuts in social programs. As it was, the leadership was unable to block an amendment by Rep. John Asbrook (R-Ohio) that would cut $3.15 billion from the Department of Health, Education and Welfare's budget.

The leadership planned to try to reinstate those funds last night.

The House by voice vote yesterday turned down an amendment by Rep. Robert C. Krueger (D-Tex.) that called for a general spending cut, but that would have exempted defense, agriculture and veterans' benefits.

The Senate passed its version of the preliminary 1979 budget two weeks ago. It called for spending of $498.9 billion and a deficit of $55.6 billion. The Senate version does not call for cuts in Social Security taxes and sets defense spending slightly higher than the House Budget Committe wants.

House and Senate conferees will get to work on ironing out the differences immediately after House approval.

By law, Congress must agree on preliminary budget targets May 15, but it now appears unlikely that the House could take action on a conference report much before May 17 or 18.