Fairfax County Executive Leonard Whorton yesterday proposed a county government budget for 1978-79 that would substantially increase spending but not raise tax rates.

But Whorton also said the $586 million budget is "conservative" and leaves no room for a tax rate cut, as some Fairfax officials have said is possible, without creating a "scenario for tax increases in 1980."

The proposed increased spending - up 15 percent over the current $506 million figure - without a tax increase reflects the strong economy of the county, according to Fairfax's financial director, James P. McDonald. In the year ending last June 30, both spending cuts and a tax increase were necessitated by the depressed housing market in the county.

"We have been through some very, very difficult tight money times," McDonald said. "This is the first year the executive can present a reasonable request to the supervisors for spending that will keep up with growth."

Even if there is no increase in the county's tax rate of $1.74 per $100 assessed valuation, the tax bill of the average county homeowner will probably continue to climb because real estate assessments have risen 8.7 percent this year. The owner of the typical Fairfax house valued at $69,000 would pay $1,305 in real estate taxes this year compared to $1,201 last year.

Despite the spending increase, Whorton's budget proposes no major new programs. It does call for three new fire stations, 93 more firemen and policemen and 91 other jobs scattered throughout county agencies. These additions would cost $2.4 million and Whorton said they are necessary because of county growth. Fairfax's population is expected to grow to 596,400 by the end of the year, an increase of 28,000 over the current population.

The single biggest increase in spending ($19.4 million) would go out for county schools, while Fairfax's share of Metro bus and subway operating costs would increase from $6.8 million to $9.5 million. Whorton also called for a 5.5 percent pay boost for county workers costing $5 million. The rest of the increases are spread over a variety of programs.

McDonald said the 15 percent increase in the budget is "distorted" because $36 million of the $80 million increase in money from bond sales that is included in this year's budget but will be spent over several years on long-range construction projects.

Whorton called for an 11 percent increase to $343 million over what was approved last year for the county's general fund, which pays for the day-to-day cost of running the county and is financed almost exclusively by county tax dollars, chiefly real estate tax revenues. Whorton said most of the increase is due to inflation and county growth.

The reminder of the budget, $243 million, comes from federal and state sources, bond sales and county fees. This money mostly pays for construction projects like the Metro subway and sewage lines.

"This budget represents a fair assessment of the needs of Fairfax County residents, but it does not have the flexibility for a (tax rate) reduction," Whorton said. "If the tax rate is cut in the current fiscal year, that will clearly establish the scenario for tax rate increases in 1980."

Across the Potomac River in Montgomery County, which is comparable to Fairfax in size and affluence County Executive James P. Gleason has proposed a real estate tax rate cut of 26 cents for each $100 assessed valuation.

McDonald said that Whorton, who, unlike Gleason, is not an elected official, cannot upstage the political role of the Board of Supervisors by "coming forward with a tax cut. That is clearly the prerogative of the Board of Supervisors." However, previous Fairfax executives have proposed changes in the county's tax rates.

Seven of the nine Fairfax supervisors have said a tax cut is possible this year.

Board Chairman John F. Herrity said this week there is enough fat in Whorton's proposed budget to allow spending cuts that would in turn leave room for a cut in the property tax rate.

Herrity called the proposed hiring of 181 new county employes "a disaster," and he said he would not support the proposed increase in the housing assistance fund from $359,000 to $788,000. The fund would provide for low-income housing assistance and a waste disposal system for the low-income Lincoln-Lewis-Vannoy community in western Fairfax.

"I think the responsible way to do this is to cut (the budget) to the point where you have some surplus so that you don't have to come back next year and have a tax increase," Herrity said.

Supervisor Martha V. Pennino (D-Centreville) earlier this week read the board a letter she received from her husband complaining about a higher reassessment that will increase the Penninos' real estate tax by $200. Higher assessments, the letter said, make the tax rate "confiscatory" and produce a "windfall for the county."

Real estate taxes finance 62.2 percent of the general fund, $212 million. About $15.8 million of the increased revenue would come from higher assessments on homes and $7.7 million would come from taxes on new homes.

Spening for the county school system ($167.5 million) accounts for nearly half of the general fund. The remainder will go for a variety of county government functions, including social and health services ($28.5 million), justice ($2.5 million), general government ($37.2) million) and public safety ($34.7 million).