Congress began its first formal skirmish over the fiscal 1980 federal budget yesterday as Democrats on the House Budget Committee, over the objections of their chairman, proposed major reductions in President Carter's defense budget, designed to pare the deficit further.

After a week of preliminary caucuses, the Democrats recommended trimming $1.9 billion in military outlays and $4.1 billion in Pentagon authority to begin new projects. They also urged denying a Defense Department request for $1.1 billion in added funds for fiscal 1979.

The proposal, if it passes, could spell trouble for Carter. The president promised members of the North Atlantic Treaty Organization the U.S. would boost defense spending 3 percent after inflation in fiscal 1980. Under the Democrats' plan, it would rise only 2.3 percent.

However, Rep. Robert N. Giaimo (D-Conn.), Chairman of the panel, said the Democrats' proposals were "certain to be controversial, and frankly more than I would recommend"-indicating the plan may face a challenge when the committee begins its drafting session this morning.

Giaimo said he personally had sought to trim Carter's defense budget only by $1.5 billion in outlays and $3 billion in new spending authority. And committee Republicans served notice they, too, would oppose any cuts that deep.

The internal squabbling marked the start of what is expected to be a week of continual battles over budget issues as the House panel and its Senate counterpart hammer out recommendations for Congress' fiscal 1980 spending and Tax-recipt targets.

The Senate committee did not make any formal recommendations yesterday, but sources indicated it was likely that that committee also would see some heated skirmishes.Committee staffers published estimates yesterday of what fiscal 1980 spending would total if current law remained intact.

The proposal by the House committee's Democrats called for an overall spending level of $532.6 billion, with a deficit of $27 billion-a red-ink figure that is $2 billion below the $29 billion deficit Carter proposed last January, and $1.4 billion below his latest revision.

Apart from the cuts in defense spending, the Democrats' proposal included $2.3 billion in additional cuts by ending grants to states under the federal revenue-sharing program, plus other reductions in monies for water projects, highway grants and research and development.

In addition, the Democrats proposed three controversial "reforms" that experts say have mixed prospects for passage-eliminating part of the impact aid to education program, making cost-of-living increases for federal employes annual instead of twice a year, and passing Carter's hospital cost bill.

At the same time, Republicans on the House panel unveiled a plan for trimming another $6.7 billion from non-defense spending while at the same time killing Carter's "real wage insurance" tax credit-slashing the deficit to $19.4 billion.

The GOP plan was drafted by Reps. Marjorie S. Holt (R-MD.) and Ralph Regula (R-Ohio). Holt argued the sharper cuts in spending "would put us within striking distance of having a balanced budget for the 1981 fiscal year. The Carter budget makes that goal unattainable in 1981."

The estimates by the Senate Budget Committee staff show that if current law remains unchanged, total federal outlays would reach $537.6 billion in fiscal 1980.

Lower estimates of the economy's likely growth tend to bloat projections of how much the government will have to spend, in part because of higher unemployment benefits. At the same time, higher inflations add to expected revenues.