The Senate Budget Committee's defense-loaded spending recommendations for 1981 came under cross-fire from both liberals and conservatives yesterday as a more domestic-oriented House version of a balanced budget cleared a major tactical obstacle.

Meanwhile, the Carter administration, also dissatisfied with the Senate Budget Committee's priorities was lobbying for Senate restoration of $3.7 billion in domestic spending that was cut by the committee as it slashed social programs to offset military spending increases.

The administration listed $500 million in aid to local government, $720 million for public service jobs, $550 million for Social Security programs, $500 million for transportation and $100 million for pollution control among its top priorty concerns.

In the Senate, Majority Whip Alan Cranston (D-Calif.), leading a liberal uprising against the Budget Committee's guns-over-butter priorities, proposed a budget alternative that would increase the committee's outlays for domestic programs by nearly $7 billion.

Cranston's proposal, which thus far has drawn support largerly from liberal Democrats up for reelection this year, would scale down the committee's proposed military outlays by $2.5 billion. But it would still provide more for military outlays than either President Carter or the House Budget Committee recommended in proposing deficit-less budgets for next year.

At the same time, two Senate Republicans found fault with the committee's proposal for just the opposite reason, endorsing the big increase for military outlays but proposing a $16.2 billion cut in the overall budget -- mostly from domestic programs dear to the hearts of Democratic liberals.

Sen. William L. Armstrong (R-Colo.) and William V. Roth JR. (R-Del.), refining earlier GOP tax cut proposals that the Democrat-dominated Congress has thus far gingerly sidestepped, said their proposal would pave the wap for a $30 billion tax cut in the 1981 calendar year.

The Senate Budget Committee has left a $10 billion "cushion" for possible tax cuts if Congress lives up to its spending self-discipline.

As the Senate squabbled, House leaders moved to keep the House Budget Committee's spending proposal for next year from nibbled to death by amendments when it comes to the floor next week.

Overriding objections from some Republicans, the Houuse Rules Committee voted to restrict the amendments that can be offered to about 10 proposed changes that represent a variety of viewpoints ranging from liberal Democrats to conservative Republicans.

In the process, the committee, protecting a careful compromise worked out by House leaders the last few days, beat back proposals to allow amendments on veteran benefits and other programs not mentioned in the approved list.

The committee did, however, agree to allow a vote on an amendment sought by a number of powerful committee chairman to strike language that would require committees to cut spending to fit prescribed budget ceilings.

The principal liberal effort to recoup some of the money the House Budget Committee cut from social spending will come from Rep. David R. OBEY (D-W-s.) who would restore $1.1 billion to domestic programs, including $500 million to aid cities. He would raise revenues by tightening the foreign tax credit and cut some administration costs in order to produce a balanced budget.

Although the Senate had been expected to act earlier this week on its budget, it now appears likely to wait for some House action, partly because of the internecine Democratic fighting over spending priorities.

Cranston's proposal totals nearly $6 billion more than the balanced budget that Carter proposed last month as part of his anti-inflation program. But it is less than the Congressional Budget Offices's previously reported estimate of what Carter's budget would cost, and estimate that is about $10 billion more than the administration caluclates.