More than 9,000 government workers here and an additional 21,000 nationwide may be furloughed next month -- losing anywhere from four to 20 days of pay -- because of the White House-Congress deadlock on an emergency supplemental bill that includes money to pay their salaries.

Agencies say that without additional funds they technically will go broke and be unable to meet all or part of their September payroll.

President Reagan vetoed a supplemental spending measure (with payroll funds) last weekend. He said it had too much for domestic spending, not enough for defense.

Congress could override the veto or come up with a supplemental the president will sign, but the Senate and House are out of town until early next week.

These are the agencies that have drawn up furlough contingency plans:

* National Aeronautics and Space Administration (reported here Aug. 22) says it may have to furlough 22,000 workers, many here, for 10 days in September.

* Federal Emergency Management Administration -- the agency designed to keep the nation running after a nuclear attack or other disasters -- says it may have to furlough 1,500 staffers up to eight days in September unless the crunch is solved.

* Office of Personnel Management's 3,500 aides, who were furloughed earlier this year, are looking at 10 furlough days beginning in mid-September.

* Smithsonian Institution says money problems will force it to furlough most workers -- about 2,000 people -- for a week beginning around Sept. 20. That could mean the shutdown of some museums or drastic cuts in visiting hours.

The Federal Labor Relations Authority, which had feared it would have to furlough 300 staffers beginning yesterday, says it juggled the books for this week but can't get past the week of Sept. 7.

* National Transportation Safety Board's 200 staffers may be forced on furlough for a week in September.

* National Capital Planning Commission may have to furlough about 50 workers later next month.

* Federal Maritime Administration says 300 of its people may lose a week's pay next month.

The Pentagon says that, by transferring funds, it will be able to avoid giving out IOUs to the Army, Navy, Air Force and Marine Corps.

While it is not immediately affected, the Justice Department, with 51,000 full-timers, has drawn up tentative plans to lay off nonessential workers later next month.

The furlough flap could fizzle if Congress gets back in time to override the president's veto, or come up with a supplemental the president will sign. But time is running out.

To anticipate your question, no, congressional and White House checks will be delivered on time.

Remember back when job-security was one of the big selling points of working for Uncle Sam?