The house Budget Committee, under strong pressure from the House leadership, reversed itself yesterday and restored to the 1978 budget funds for water resource projects that President Carter wants to kill.

In a surprise vote Monday, the committee overrode the objections of Majority Leader Jim Wright (D-Tex.) and Chairman Robert N. Giaimo (D-Conn.) and trimmed $280 million from its tentative 1978 budget to prevent Congress from restoring any dams or other water projects that the President opposes.

But two Democrats - Thomas L. Ashley of Ohio and David R. Obey of Wisconsin - switched their votes, and Rep. Omar Burleson (D-Tex.), who did not vote Monday, voted to restore the funds yesterday. So the narrow 13-to-11 victory Carter scored Monday turned into a 14-to-11 defeat yesterday.

The committee approved a move by Wright to return $265 million of the $280 million it cut Monday. Earlier this month, in probably the biggest political setback the fledging administration has faced, the Senate overwhelmingly rejected any of the $289 million in cutbacks proposed by Carter.

The House Budget Committee again rebuffed Wright's attempt to boost the level of defense spending closer to the $111.95 billion recommended by Carter in his Feb. 22 budget proposals. The committee has decided to spend $2.3 billion less for defense than the President proposed in the federal spending year which begins Oct. 1, 1977.

The committee also rejected a move by Rep. Otis Pike (D-N.Y.) that would have put it on record as opposing the recent 29 per cent congressional pay hike and putting congressional salaries back to their 1976 level at the start of the next fiscal year.

The committee instead adopted a substitute by Rep. Paul Simon (D. Ill.) which simply said it opposed any cost-of-living raises in October.

The committee also added $550 million to the President's projected unemployment compensation outlays because the committee anticipates unemployment will be higher than Carter does.

Congress is in the second year of a new budget process which forces it to determine how much it wants to spend and tax overall and how it wants to allocate its spending among various priorities such as defense, education, income security or health.

The House is in the process of deciding a tentative budget for the next fiscal year, and the Senate begins work on its version today. By May 15 Congress must agree on a tentative budget, and by Sept. 15 it must formulate a final taxing and spending agenda. The President still proposes a budget for the country, but the final version is Congress'.

The committee's decision Monday to back the President's deletion of water project money was a surprise in view of the strong leadership opposition.

Rep. Butler Derrick (D-S.C.), whose move to cut spending was approved Monday and reversed yesterday, argued that unless legislators could "discipline themselves in those things that affect us directly," such as the water projects, Congress will never be able to get federal spending under control.

Wright said he has no objection to the President's re-examination of the 30 water projects, but he said that by deleting the funds, the committee is prejudging the situation. The total cost of the 30 projects is $530 million in fiscal 1978 and could run as high as $7 billion before the projects are completed.

But, as Derrick noted, if the President should approve all of the projects - and he has promised a decision by mid-April - the funds could be restored to the fiscal 1978 budget before Congress passes the May 15 budget resolution.

Ashley, who reportedly is the leading candidate to head a new House committee to deal with President Carter's energy program, told reporters he found convincing Wright's argument that deleting the funds now would prejudge the President's decision.

The Ohio Democrat acknowledged that White House officials had been in touch with him Tuesday night to urge him to "hang touch."

Last night the House committee completed action which resulted in total spending of $462.3 billion next year and a deficit of $64.3 billion. President Carter, on Feb. 22, proposed to spend $459.4 billion and projected a deficit of $57.8 billion.