Departments and agencies across government are drawing up plans to begin shutting down operations next week or to start furloughing nonessential workers (perhaps even before Christmas) for short periods of time, depending on what happens with their budgets this week.

The stopgap resolution allowing agencies to keep running in absence of approved budgets expires Friday midnight for most operations. Unless Congress and the White House reach agreement on a new resolution, agencies will be required to stop most normal work Monday. Employes will be limited to battening-down-the-hatches chores. Technically when agencies run out of money workers aren't even supposed to answer phones unless it is part of the shutdown.

Even if the White House and Congress resolve their differences over spending levels -- President Reagan has warned he will veto anything that does not provide for a 5 percent spending reduction in programs he wants cut back -- there is the distinct possibility that some agencies still will have to furlough people to help trim their share of the $190 million Uncle Sam spends each day in civilian federal payrolls.

Examples of what is happening across the government because of the budget confusion:

* Bureau of Labor Statistics has a contingency plan to furlough people for up to nine days if its budget is cut. BLS has about 1,900 workers, including 1,200 here. Although agencies are supposed to give workers 30 days' notice of intent to furlough, they can order them on short notice in emergency situations. The BLS plan, typical of those drawn up by many other departments and agencies, has not yet been cleared by the Labor Department or the Office of Personnel Management.

* Office of Management and Budget issued a reminder to agencies and departments yesterday reinforcing a Justice Department ruling (from the Carter administration). It says that most agencies must limit themselves to shutdown duties starting Monday if the continuing resolution is not approved. Excluded from the shutdown are national defense, life-saving and property protection operations.

* General Services Administration has advised key managers that it will begin talks with unions about a "projected" layoff of 911 workers, including 330 here, because of budget problems. If the RIFs come, the first workers would be separated as early as February.

Meantime, Reps. Geraldine Ferraro (D-N.Y.) and Patricia Schroeder (D-Colo.) have sent warning letters to federal agencies telling them NOT to fire or furlough anybody until Congress acts on their budgets. They chair subcommittees of the House Post Office-Civil Service Committee and want to make sure that nobody is fired or put on LWOP based on what the boss thinks Congress might do (or not do) to his budget.