The American Federation of Government Employees has been given until Monday to repay the government $1.1 million that was used for union business rather than the administration of its health plan -- or be cut out of the government's health insurance program next year.

An AFGE spokeswoman said yesterday that the 180,000- member union is "confident" the issue will be resolved and that AFGE's health plan will be among those offered several million U.S. workers and retirees during the Nov. 9 to Dec. 11 open enrollment period. During that open season federal workers pick which of the nearly 300 plans in the program they wish to carry in the coming year.

Despite AFGE's optimistic forecast, officials of the Office of Personnel Management said the union failed to respond to several warning letters about the repayment.

They say AFGE's health plan will not be listed in the insurance guide to the open season that may be released Friday. An OPM spokesman said that AFGE has until Monday to repay the money so that it can participate in the federal health plan.

The federal health program, which allows employes to pay premiums via payroll deduction, is the nation's biggest company health plan. It covers 12 million workers, family members and retirees, and helps pay the medical and dental bills for more than half the people in the Washington area. AFGE's plan now has just over 31,000 members.

AFGE's financial problems surfaced in May when it was revealed that an OPM audit showed that during the past five years the union has spent about $5 million for administrative purposes but had received about $6 million for that purpose from the government. AFGE President Kenneth T. Blaylock said at the time there had been some "bad record- keeping" in the past that allowed the funds to be commingled with the union's regular operating funds.

Blaylock, who was out of town yesterday, said in May that AFGE would repay the money as soon as OPM told the union how much was owed. But OPM officials say the union failed to respond to a series of warning letters about the problem, the most recent dated Aug. 20. An OPM official said yesterday the union had requested a meeting on the issue, but it still must come up with the money by Monday or be out of the program.Privatizing Jobs

The Federal Employees News Digest says the Reagan administration is planning a final drive to require federal agencies to identify civil service functions that could be performed by private contractors. The weekly newsletter says that the draft of a proposed presidential order to federal agencies is being circulated to top federal officials.

The administration has tried, with mixed success, to force the government to eliminate functions that compete with the private sector. At one point the White House estimated that as many as 600,000 of the government's 2.8 million jobs fell into that category. But congressional Democrats have blocked most efforts to contract out major federal functions, and the number of civil service workers has increased since Reagan took office.