Fifteen thousand government workers, about one-third of them here, will be furloughed within the next two weeks unless Congress and the White House reach quick agreement on emergency funding to allow agencies to meet their payrolls through the rest of the summer.

The tug-of-war between the Reagan administration and the Democrat-controlled House has already meant a 50 percent pay cut for nearly 400 aides at the Merit Systems Protection Board. Most of the MSPB people started furloughs last Tuesday because of the money shortage.

Portions of other departments--Labor, Health and Human Services, Treasury, Commerce and Education--say they will have to furlough people unless their emergency supplemental appropriations are cleared soon.

President Reagan has already vetoed two emergency supplementals approved by Congress, on grounds that they contained budget-busting spending riders. The House today will attempt to override the latest veto. If it fails to override, it will consider, later on, a slimmed-down Senate-passed supplemental okayed by the president.

But time is short, especially for workers in three Labor Department units--the Bureau of Labor Statistics, Employment and Training Administration and Employment Standards Administration. They are due to begin furloughs of up to 22 days starting Monday unless they get relief this week.

The Bureau of Alcohol, Tobacco and Firearms of the Treasury Department says it must begin furloughing most of its workers unless the supplemental is approved by July 23.

Things could get worse at the MSPB, where people are already working half days, every other day or a 20-hour week. They will get their first paychecks reflecting a 50 percent pay cut next Tuesday. Worse yet, officials say that indefinite furloughs for most of the staff may be ordered later this month unless the emergency money bill is passed soon.

Some of the agencies on furlough, or facing furloughs, are already starting to lose some of their best, and most mobile, people.

The Defense Department is getting lots of inquiries, and some new recruits, from specialists in non-Defense agencies. Some of the most mobile people, with transferable and marketable skills--from secretaries to statisticians, attorneys and computer experts--are fed up with the constant threat of RIFs and/or furloughs. Many are eager to work for Army, Navy or the Air Force, whose civil servants can still watch TV news or read the morning paper without suffering heartburn or heart failure.