In what one angry liberal called part of a Democratic Party "identity crisis," the heavily Democratic House yesterday rejected four proposals to restore funds for social programs that are being cut to balance the budget next year.

In the closest vote, 201 to 213, the House rebuffed President Carter and some of its own Democratic leaders in spurning $1.1 billion more for domestic spending than the House Budget Committee recommended in cutting Carter's January budget.

This domestic spending increase proposed by Rep. David Obey (D-Wis.) -- largely for aid for cities, youth programs and other social endeavors -- would have been financed largely by an $800 million increase in oil company taxes through modification of the foreign oil tax credit. It alternately was defended as an essential minimum for domestic programs and decried as a "very tempting siren's song" and a "chief's brew of table scraps." d

In the other votes, the House rejected:

By 74 to 313, a Black Caucus proposal to increase domestic outlays by $5.4 billion, largely by lopping $3.1 billion off the projected increase in defense spending.

By 65 to 352, another liberal proposal to add $5.3 billion in domestic spending and finance it by plugging so-called tax "loopholes" that Congress has shown a reluctance to tamper with in the past.

By 70 to 336, the most far-reaching proposal -- to add $18.1 billion in restoring all the cuts from Carter's January budget, financed by tax increases.

Cheered only by the closeness of the Obey vote, the liberals today face their most critical test: a move by millitary-minded conservatives to cut $5.1 billion from domestic outlays proposed by the Budget Committee and use the money for defense.

The Budget Committee held its bipartisan base of moderate-to-conservative support in yesterday's votes, effectively consigning liberals to a minority position. However, 30 Republicans abstained on the Black Caucus proposal, in effect having it both ways on the issue, and 36 Republicans supported Obey's proposal.

In an effort to help fight inflation by balancing the 1981 budget, the budget committees of both houses proposed billions of dollars in cuts from domestic spending that Carter recommended in his January budget, heavily pruning some social programs that have been dear to the hearts of Democratic liberals. The Senate committee's cuts were especially severe, although House liberals complained that their committee's cuts were draconian as well.

House Budget Committee Chairman Robert N. Giaimo yesterday defended the committee's proposal as balanced, saying, "You can't make an omelette without breaking some eggs, and you can't balance a budget without making some [spending] reductions."

But Rep. Ronald V. Dellums (D-Calif.) said the House was trying to balance the budget "on the backs of the poor," and Rep. James L. Oberstar (D-Minn.) said the House is seeking no sacrifice from corporations or the wealthy. "Little is asked of those who already have much," said Oberstar.

In an earlier vote, the House refused to rescue the $1.7 billion state revenue-sharing program from the budget guillotine and thereby reverse one of the principal economy moves recommended by the Carter administration in both the House and Senate Budget committees.

By a 192-to-225 vote, it turned down a proposal by Rep. Barber Conable (R-N.Y.) to keep the no-strings-attached revenue-sharing program started during the nixon administration, and cut categorical grants by $1.7 billion instead.

Conable's proposal was strongly backed by the nation's governors but opposed by many liberal groups that feared cuts in grants for social programs.

Conable argued that continuation of revenue sharing would help neutralize the "poison of centralism" and strengthen state and local governments. Foes of the program appeared to make more points, however, by citing the long list of categorical grant programs that might suffer -- from flood-control projects to aid to minority-run businesses.

"Hell hath no fury like a vested interest masquerading as a moral principle," said Rep. Clarence Brown (R-Ohio) in supporting Conable's ill-fated effort.