Argentina and its key bank lenders have failed to meet their self-imposed Christmas deadline for a $4.2 billion worldwide financing package.

When the outlines of the agreement between financially troubled Argentina and its major banks was announced Dec. 2, many had hoped that enough of the country's 320 lenders would come on board by Dec. 25 to bring to a close the first phase of the so-called Latin American debt crisis, which began in August 1982.

But Argentina, which owes banks about $2.5 billion, has met considerable resistance, especially from European banks, sources said. Bankers are angry because Argentina has dragged its feet for more than two years, while other debtor countries -- such as Mexico and Brazil -- took hard, politically difficult steps to put their economies back in shape, reduce their need to borrow and increase their export earnings.

Argentina, which went through a change from military dictatorship to a democratically elected government late last year, had protested that it could not take the same kinds of belt-tightening measures for fear of endangering the new democracy.

During the two years, however, Argentina's overdue interest has grown steadily, and now it owes banks more than $1.2 billion in back interest payments. It also owes about $10 billion in overdue principal payments. The Dec. 2 agreement not only called for $4.2 billion in new funds for Argentina, but also would stretch out for 10 to 12 years repayment of about $13.4 billion in principal payments that already have come due or will by the end of 1985. Argentina's total foreign debt is about $45 billion.

The debtor country and its 11 major lenders, led by Citibank executive William R. Rhodes, set the Christmas deadline so that the International Monetary Fund (IMF) could approve its part of the Argentine rescue package by the end of the year. In return for agreeing to major changes in its economic policies -- mainly steps to reduce its 700 percent inflation rate -- Argentina is supposed to receive $1.4 billion from the IMF next year.

But on Jan. 1, Argentina's borrowing limit from the international rescue agency will fall roughly $100 million as a result of new rules pushed through last year by the United States.

Banking sources said they still hope to bring enough of Argentina's 320 lenders on board by Dec. 28 to persuade IMF Managing Director Jacques de Larosiere to submit the $1.4 billion IMF loan to his agency's executive board Friday.

In an apparent attempt to entice more banks to come on board soon, Argentina announced yesterday that as soon as the banks and the IMF approve its financing plan, the country will repay $850 million of the overdue interest, $100 million more than it pledged Dec. 2. If the interest -- about two-thirds of the total overdue -- is received by Dec. 31, the banks can count it in their 1984 earnings.

The U.S. Treasury has promised a temporary $500 million loan to Argentina as soon as the IMF board approves the package. That loan, most of which presumably would be used to pay interest, will be repaid as soon as the IMF disburses funds to Argentina.