About 300 adults and 300 children demonstrated yesterday on the west terrace of the Capitol in opposition to $78 million in cuts the House Appropriations Committee has recommended in the District of Columbia's proposed 1980 budget.

The $1.4 billion proposed operating budget will be voted upon by the full House Wednesday. At issue is the committee's recommendation that the federal government contribute $191.5 million towards the city budget. President Carter has proposed a federal payment of $317 million.

As tourists watched, about 20 speakers attacked the budget reductions. Several excoriated the subcommittee chairman who first proposed the cuts, Rep. Charles Wilson (D-Texas).

Wilson's office said the congressman had not returned from Texas at the time the demonstration was held.

Although most speakers said the budget cuts would bit hardest at social programs, an Appropriations Committee aide said none would be cut below its funding level for this year. Day care, one of the most frequently cited programs, would get an increase of $250,000 above this year's $9.1 million outlay, or about half what the city had sought for 1980.

Del. Walter E. Fauntroy (D-D.C.) who spoke at the demonstration, cited other cuts, such as the denial of funding for a 100-bed expansion at D.C. Village, the city's home for the elderly where, he said, there is already a backlog of 500 applicants.

An aide said Fauntroy would make a token but probably futile effort to persuade the House tomorrow to give the city substantially more support. The aide said the real effort to win back the budget cuts will be made later in the Senate which still has to study the budget and come up with its own recommendations.

Fauntroy said he will soon introduce a bill in the House that would give the city full control over its own budget, along with an assured federal payment each year. City Council member Btty Ann Kane (D-At Large) supported this approach at the demonstration yesterday, calling the present system of home rule "home fool."

Yesterdays, rally was organized by a newly formed group called Citizens to Save the D.C. Budget, headed by Willie J. Lynch Jr., board chairman of the Washington Area Council on Alcoholism and Drug Abuse. He said the number of adult participants was smaller than the 500 to 1,000 that had been expected.

One German tourist, Maria Schaefer, who listened to the speeches for about 10 minutes, asked: "Why so few people? If that were in Bonn, there would be a lot of people."

Edna Itzhaki, a visitor from Israel, said she was impressed by the rally. "It it nice to see the black people and the white people all together in the demonstration," she said.