When Denise F. Shaw looks at homeowners in suburban Fairfax County tending tomato plants and throttling crab grass, she sees "urban farmers."

Powerful state Del. Frank Slayton, a son of rural, tobacco-growing Southside Virginia, sees red. "Urban farmers?" he sniffs. "That's like rhinestone cowboys."

Slayton, a senior member of the House Appropriations Committee, would like to tear much of a $25 million state extension program up by the roots and toss it away -- including some of Fairfax's $630,000-a-year share, which Shaw oversees.

His complaint: The program has grown faster than dandelions on a summer lawn, spending more than half its budget in areas where the residents' idea of working the land is growing fruit trees in the backyard.

Less than 50 percent of the budget is devoted to farming, according to Slayton, although the program was originally intended to help farmers bolster their output.

Even worse than lawn control tips, Slayton discovered county extension agents have offered courses in finger-painting and how to conduct a garage sale and have even sponsored golf tournaments. Fairfax, with its high rises, tract housing and shopping malls, has 11 fulltime agents, more than other other county in the state.

"I live in a county, Halifax, and we grow a lot of corn and are the second biggest tobacco producer in the state and we have only seven agents," Slayton grouses.

But Fairfax's Shaw defends her turf.

"It's the way you look at it. Take a hundred-acre farm and break it into quarter-acre lots. On each lot you have someone fertilizing grass, growing shrubs and bushes, perhaps a few fruit trees, and probably tending a small vegetable garden in back . . . It doesn't bother me that we have the most agents. We have a problem meeting the demand for the 11 [agens] we have."

That won't stop Slayton from trying to prune the program during the current legislative session in Richmond. Slayton is determined to see the extension service "vastly reduced" he says, and has picked up support from a surprising ally -- Fairfax Republican Del. Vincent F. Callahan Jr.

"The extension program in the state has gotten out of hand," agrees Callahan. "There seems to be a lot of make-work."

Even some federal officials share that view. "I would have to admit the mission of the [extension] service is a bit fuzzy," says Anson R. Bertrand, director of the Agriculture Department agency that runs the service nationwide. But, he adds, Congress has mandated some of the urban programs carried out by extension agents.

In populous Alexandria, where four agents, among other things, run 4-H courses enrolling 1,623 children in everything from archery to clothes-making to dog care, the program had won an unexpected friend.

The city's vice mayor, Robert L. Calhoun, says cutbacks like those envisioned by Slayton would be unfortunate. "When I first came to the City Council, I viewed this program with a degree of skepticism. Why is the extension service, with its agricultural base, involved in the cities? But I've come to be a big supporter," he says. "They're reaching children in the inner city that other programs don't reach. They are filling gaps. They are not frivolous."

Fairfax's Shaw agrees. Everything has changed since the extension program was created in Virginia in 1914," she says. "Our role is to meet the needs of the people where we work."

But that role may soon be redefined. Extension officials, aware of the budget-cutting threat in Richmond, have submitted a redrafted statement of the service's mission to the administration of Gov. John N. Dalton. Under the proposal, farm productivity would get more emphasis.

"We will be more restrictive in the future," says service director William R. Van Dresser. "The message on our mission to the localities will be extremely clear."

Meanwhile, Slayton, annoyed that the redrafted mission has not been delivered to legislators by the date promised, says he is drafting his own sharply curtailed mission, leaving some of the extension services to community colleges.

To which Fairfax County's director, Shaw, says, "How is a college to answer a caller who is interested in canning and wants to know , 'How long do I pressurize my beans?'"