The Vienna Town Council needed just 45 minutes Monday to discuss, argue about and accept five amendments to the town's budget before ratifying a $9 million fiscal package that will leave the town property tax rate at the current level.

The original fiscal year 1985-1986 budget, presented to the council by Town Manager John Schoberlein on May 10, contained a proposal to set taxes on property at 37 cents for every $100 of assessed value.

In three previous work sessions, the council had reduced that figure to 34 cents, and Monday night it agreed to a compromise on one of six amendments presented by council member Ross Buckley that will leave the tax rate for every $100 in assessments at 33 cents.

But that agreement was reached only after council members had grown weary and tempers had begun to wear thin because the budget, at the suggestion of council member Robert Robinson, had been pushed to the end of the council agenda.

Most of more than 50 people who attended the meeting were there to comment on six items concerning development and construction plans.

Arguing that the budget should be considered first, Buckley said, "The most important task for this Town Council is the budget and the setting of the tax rate for fiscal year 1986."

But despite the postponement of four additional agenda items, work on the budget did not begin seriously until about 1:20 a.m. At 2:04 a.m., the council unanimously passed the amended measure.

Before consideration of the budget proposals was cut off early in the evening, it became apparent that the council, in what one member called "belt tightening," wanted to garner more savings than those proposed and was committed to settling the matter in one council session.

"I think there are some savings that can be made," Mayor Charles Robinson told Vienna resident Betty Stewart, who complained to the council that a rise in the property tax rate was not justified in light of the 3 to 5 percent increases in Fairfax County property assessments.

Robinson said, "I think all of us were a bit aghast at the possibility of a 3- or 4-cent increase in the real estate tax rate ."

Buckley then presented a package of six amendments that he said would enable the town to "expect additional savings of approximately $130,000," allowing a lowering of the tax rate to 32 cents per $100 assessed valuation.

In the early-morning hours, the council voted with Buckley quickly and in succession to delete a $16,360 microcomputer from the management services request and to reduce town contributions to the police pension fund by 6.3 percent for a savings of $53,000.

The council also agreed to exact a $14,000 savings by deleting Public Works' requests for a construction trailer and a one-ton dump truck.

The property tax decision -- reached only after Buckley agreed to give up the 32-cent tax proposal and an amendment that would have cut the proposed $93,050 contingency fund by more than $14,000 -- is estimated to produce more than $2.1 million.

Mayor Robinson, though in favor of a lighter rate than originally proposed, expressed concern about lost revenues from the continuation of the current tax rate.

"I have some real questions as to if we'll be able to do it on the same tax rate," he said, before being assured by town manager Schoberlein that the rate continuation would work because of expenditure cuts.

Other major provisions in the Vienna town budget for the fiscal year that will begin July 1 include authorization of $2,000,900 for Public Works, including an increase in street maintenance funds of $43,090 over the present budget, and an increase in the police and volunteer fire service budgets to $1,430,868 -- $195,842 more than was budgeted for 1984-85.