The House yesterday brushed aside a Republican attempt to cut spending this fiscal year as it squared off for a high-stakes battle over how to balance the 1981 budget without stepping on too many political landmines.

This came as President Carter waded into the House budget fight endorsing a proposal by Rep. David R. Obey (D-Wis.), to increase 1981 domestic spending $1.1 billion over what was recommended by the House Budget Committee, including $500 million in aid to cities. Obey would pay for the increase largely through cutting foreign tax credits for oil companies.

In the House, the Democratic leadership won an early tactical victory in fending off a motion to allow unlimited amendments to the Budget Committee's proposal, including one by Rep. Robert H. Michel (R-Ill.) to put a $565.6 billion ceiling on 1980 spending.

Michel's total was $6 billion less than the $571.6 billion that House Budget Committee Chairman Robert N. Giaimo (D-Conn.) is recommending as the lid on spending for the fiscal year that began last Oct. 1.

Complaining the Giaimo's proposed spending total has grown $25 billion beyond what Congress approved as a lid late last year. Michel said Carter should be directed to impound, or refuse to spend, any money that exceeds $565.6 billion.

Michel's effort was doomed when the House, on a procedural vote of 249 to 153, signaled that it wanted to rstrict itself to 11 amendments that had previously been cleared by the House Rules Committee as a balanced set of alternatives on spending priorities.

The Rules Committee's agenda of amendments precludes spending reductions for 1980, but, on paper at least, it would assure a balanced budget for 1981 for the first time in 12 years. At the same time it would give the House broad latitude in determining spending priorities within this limit, and major fights are expected over how to apportion the austerity, principally between domestic and defense needs.

The critical vote in the House is expected on an amendment by Reps. Marjorie S. Holt (R-Md.) and Phil Gramm (D-Tex.) to add $5.1 billion to the Budget Committee's recomendation for defense spending and to subtract a comparable amount from government operating expenses, foreign aid, regulatory programs, public service jobs and food stamps.

Among liberal proposals to increase domestic spending, Obey's amendment, newly strengthened by administration support, is viewed as having the best change of passage, although it is running against an austerity-and-defense tide in Congress.

The House Budget Committee has recommended spending of $611.8 billion for 1981, roughly in line with the revised spending program Carter sent to Congress last month after he decided to fight inflation by balancing the budget. It included $147.9 billion for defense.

By contrast, the Senate Budget Committee's $612.9 billion budget proposal includes $155.7 billion for defense, an increase of $5.2 billion over Carter's recommendation and $7.8 billion over the House committee's proposal, with offsetting cuts in domestic spending.

In the Senate, liberals have mounted a campaign to restore some of the money cut from domestic programs, with little success so far.

If the House sticks by its Budget Committee's spending priorities or adds to its proposed domestic outlays, the Senate liberals could expect some gains in a House-Senate conference on the budget resolution. But if the Holt-Gramm amendment to increase military spending is passed, sharp domestic cuts would be virtually assured.

Even the House committee's proposal has triggered outcries from groups ranging from governors and mayors to labor union officials for its proposed elimination of state revenue sharing, cuts in jobs and welfare programs, curtailment of Saturday mail deliveries and other austerty measures.

Under congressional procedures, this first budget resolution merely sets targets, and is nonbinding. A theoreically binding resolution for fiscal 1981, which starts Oct. 1, will be passed in September, after Congress has acted on specific 1981 appropriations bills.