Top federal executives have a 5.5 percent increase in their pay scales. The question this week is whether they can keep it.

The Senate and House resume their budget battle today. Hanging in the balance are overdue, 1978 increases for 22,000 top federal executives as well as budgets for most major departments that have been technically broke since Oct. 1, when the new fiscal year began.

One of the big issues warring members of Congress must resolve is whether to allow the $47,500 pay lid for top federal executives to move up 5.5 percent, to $50,100. Congress approved the increase last year, but specifically denied agencies authority to pay it. That "cap" at $47,500 expired when the old fiscal year ended Sept. 30.

The problem is that Congress hasn't decided what to do about raises for itself -- raises that total 12.9 percent. That increase represents the 5.5 percent Congress denied itself in 1978 plus the compounded value of a 7 percent raise Congress is due this year as part of the overall federal-military pay increase.

The House thought it has a way out of the politically sticky situation. After many failures, it finally approved language -- in that legislative appropriations bill -- that would have allowed itself and top federal officials to take the 5.5 percent raise from 1978, but not get the 7 percent raise due this year.

Unfortunately for federal executives (and members of Congress who want a raise) the Senate didn't go along. It approved the 5.5 percent for government supergraders, but denied it to members of Congress. Meanwhile -- thanks to a constitutional provision prohibiting anybody from cutting federal judges' pay -- top judges have come due for the full 12.9 percent raise.

First action will probably come in the House, which must act on a Senate-passed legislative branch appropriation bill. It carries the new 5.5 percent rates for federal executives, but no increase for members of Congress. That means the House must again bite the political bullet and accept raises for itself or, insiders believe, kill off increases for everybody.

The Senate and House could decide to deny all top officials raises this year, maintain the $47,500 pay lid for federal officials, and hold their own salaries to $57,500. Only the judges would be exempt from the pay denial.

Congress could approve the 1978 5.5 percent raise for itself. That would mean a 5.5 percent raise for federal executives, to the $50,100 ceiling. It would not be a "new" raise, but rather approval of the 5.5 percent approved -- but never paid -- last year.

Federal officials watching the pay mess believe government executives will be lucky to keep what they have got: That is the "new" rates set in 1978 but frozen until the fiscal year started.

Congress can allow the 5.5 percent raise to stand simply by authorizing agencies (which have already programmed the higher, 5.5 percent amount for executives into their computers) to pay those 1978 rates. Officials say they hope adjustments can be made so that federal executives in the top step of Grade 15 will be allowed to move up to full 7 percent raises, provided they do not exceed rates for their bosses who would be held to 5.5 percent.

Carter administration officials are optimistic (they have to be) that Congress will allow the 5.5 percent executive raise to stand. But Captiol Hill experts are more pessimistic. They believe all the pay raises for executive level bureaucrats will be cancelled unless Congress can find a diplomatic way to give itself the same 5.5 percent increase.