With the Democratic Party $3.6 million in debt, political fund raising, Carter style, began in earnest yesterday.

Giving without getting anything in return was the message of the day.

The President appeared to speak and shake hands at a luncheon of 300 members of the Democratic National Finance Council, a newly formed group whose members are pledged to raise from others or contribute themselves $5,000 a year for four years.

Carter told them raising $20,000 over four years was "not a difficult task if your heart is in it."

His audience included a large number of longtime Washington lobbyists and well-known past big contributors such as Dr. armand Hammer of Occidental Petroleum. They gave him a warm standing ovation when he concluded saying Americans "expect to give much more than they ever hope to receive."

The Finance Council is just one element of an ambitious, complex Democratic big-money fund railing effort designed to wipe out the party debt by this fall and build up a 1980 campaign war chest of $4 million.

Joel McCleary, the party's 28-year-old treasurer, outlined the goals of the program at a meeting of the council's executive committee yesterday morning.

Executive committee members, under the new program, are individuals who have pledged to give or raise $5,000 themselves as well as recruit nine other $5,000 donors for the council. Under the federal election law, an individual can give $20,000 a year to the national party organization, but only $1,000 to a candidate.

Jess Hay, a banker from Dallas and chairman of the council, called the pyramid fund-raising operation a new dimension in Democratic Party involvement for the business and professional community.

One executive committee member asked Hay, "What do we tell prospects they will get for their $5,000.

Hay's answer was, "Nothing, except a sense of participating in something worthwhile."

Hay did stress that there would be special seminars with Cabinet members and other government officials for the $5,000 donors, but characterized such meetings as "dialogues."

Patrick O'connor, a longtime party fund-raiser, Washington lawyer and now council executive committee member added: "You are going to get first-hand, inside information from Cabinet members."

Yesterday's afternoon session proved O'Connor's point. At the council's 40-minute question-and-answer session with White House energy adviser James R. Schlesinger, the members learned in advance about the administration's plan to ask Congress to make rebates on small cars retroactive to the end of April.

Later in the afternoon, Bert Lance, director of the Office of Management and Budget, took 30 minutes of questions. In between, White House aide Hamilton Jordan made a brief appearance.

The smoothness of yesterday's sessions and the fact the Democrats control the White House blurred for a moment their tight financial position.

As of April 15, there was only $6,000 cash on hand, according to Treasurer McCleary. Fund raising for the first four months of the year was running nearly $500,000 below what was projected just two months ago.

Meanwhile, the Democrats are under a court order to pay $60,000 a month to american Airlines to meet debts incurred in 1972. Last week, a lawyer for telephone companies also owed money from 1972 was told by the Democrats that his payments may be delayed this month.

Another $200,000 in bank loans, made in December and January to cover the transition and inaugural period, are coming due. In addition, the party owes Gerald Rafshoon and Patrick Caddell, Carter's advertising man and pollster, a total of $670,000 from the 1976 campaign, according to documents made available by McCleary.