Congress broke out the red ink yesterday and began the politically distasteful chore of writing a deficit into the balanced budget plan that it adopted only two months ago for fiscal 1981.

"The balanced budget we hoped for then is out of reach now; everyone knows that," said Senate Budget Committee Chairman Ernest F. Hollings (D-S.C.) as the committee began drafting a second and theoretically final budget for the fiscal year that starts Oct. 1.

It was with much fanfare that Congress in June adopted a tentative budget plan that contemplated a modest surplus for the first time in 12 years. But the black ink was hardly dry before soaring unemployment rates threw the budget out of balance by reducing tax revenues and adding to the cost of social services. A deficit of about $30 billion -- even without a tax cut that is considered likely for 1981 -- is now projected by the Carter administration and by congressional budget experts.

Hollings scheduled long drafting sessions in hopes of completing committee work by the end of this week, even though it now appears doubtful that Congress will finish work on the budget before the Nov. 4 election.

"Even if Congress does not adopt this resolution by Sept. 15" as required by law, Hollings told the committee, "failure to report it now will leave Congress without any constraint on spending bills. By reporting a revised budget now, we can use it to control spending for the rest of the year."

The House is mired down in a politically charged dispute over spending cuts that were ordered in the first resolution, forcing the House Budget Committee to delay its work on the second resolution.

As a result, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said recently that a post-election session to deal with the budget is a "near certainty." Such a "lame-duck" session had been considered likely by some lawmakers even before the impasse because of the political difficulty of voting to convert a balanced budget into a deficit budget just before election time.

The deadlock arose over an 8-to-7 vote by the House Rules Committee to open a nearly $10 billion package of spending cuts and revenue measures to a floor amendment aimed at preventing a cutback in cost-of-living increases for federal employe pensions. House budget leaders feared such an amendment could unravel the whole package. The Rules Committee will meet again today on the issue, but budget leaders indicated they were not optimistic about a breakthrough.

The Senate, however, cleared a self-imposed hurdle of its own when the Appropriations Committee settled a dispute on spending priorities that was threatening to hold up action on money bills that are piling up all over Capitol Hill.

The dispute arose last month when Appropriations Committee Chairman Warren G. Magnuson (D-Wash.) proposed to allocate money differently from the outline proposed by Hollings' Budget Committee. This prompted an angry protest from Hollings, who had led the campaign for a big defense spending increase in the budget, that Magnuson was seeking to divert $4 billion from defense to domestic programs.

Magnuson then proposed to put $3.7 billion back into the defense kitty but, in the process, shift money from the jurisdiction of several subcommittees responsible for domestic spending, prompting protests from them, too. Sen. Thomas F. Eagleton (D-Mo.), chairman of the Appropriations agriculture subcommittee, complained in particular that the Pentagon would get money for civilian pay increases while domestic agencies would not.

At yesterday's meeting, Hollings suggested that the committee simply follow the Budget Committee's blueprint. Eagleton complained that this would turn the Appropriations Committee into a mere "rubber stamp" of the Budget Committee, a touchy issue in the turf-conscious Congress. Finally, Sen. Henry Bellmon (R-Okla.) resolved the largely Democratic dispute by proposing that $1 billion be shifted from Magnuson's labor-human services subcommittee to agriculture and urban programs. The committee wearily accepted the proposal.