Montgomery County's dilemma over one of its biggest problems -- how to dispose of its citizens' trash -- has spawned a political movement led by an ex-Redskins lineman that includes a $110,000 treasury and a citizens' group that won't give up despite its slim chance of success.

Since 1965, the county has spent more than $65 million for projects and studies on solid waste, chiefly because the county's 580,000 residents generate enough trash daily to fill a pit the size of a three-foot-deep football field.

The citizens' group is fighting the county's planned May 1 opening of a solid waste landfill in Laytonsville, fearing that the dump will pollute local well water.

To that end, the Greater Laytonsville Civic Association, a group of about 250 people who formed to fight the landfill after the county selected the site in 1977, have held a marathon series of fund-raisers, dinners, raffles and "Monte Carlo" nights. The association's president, former Washington Redskin Ray Schoenke, has bank receipts that show that the group has raised $110,000. The group also has filed a lawsuit in Montgomery County Circuit Court charging that all environmental questions regarding the dump have not been settled.

The association has made its name known by organizing a march on the statehouse in February, complete with some 300 picketers. A small contingent of Laytonsville citizens also attempts to keep the issue alive each week at the county council meeting, an effort that Council President Neal Potter says takes 30 to 90 minutes of the day-long agenda.

The group's relentless efforts are being noticed, although few observers believe the association can stop the landfill.

"I think they have been effective in the past, but I wonder if they started early enough," said Paul Clark, chairman of the Montgomery County Republican Central Committee. "It would be very hard for them to get it stopped at this point."

The money that's been raised is being used to hire Fred C. Hart Associates, a New York firm experienced in waste dumps, to plead the citizens' case before the press and to appear as an expert witness in the lawsuit. The firm plans a press conference this week to declare that the present design of the landfill is unsound. Many of the landfill's neighbors insist that the landfill needs to be lined with clay to prevent contaminants from leaching into the ground water.

"We're going to the wire on this," said Schoenke, as he doodled on a "No More Mr. Nice Guy" scratchpad in his Bethesda insurance firm recently. "Our claims have been dismissed because we are not technical people. So we have gone out and gotten the technical people."

Schoenke, 40, who has lived in Laytonsville since 1974, also has plans for the association to form a political action committee to try to influence or field its own candidates for county office. Schoenke, who ran George McGovern's campaign in the county in 1972, is flirting with the idea of running for office, although he will not commit himself. "I'm extremely disappointed in the leadership of the county," said Schoenke. "(Laytonsville) has been had . . . And when we complain, we get deaf ears."

Because of Shoenke's friendship with the president of a Washington political consulting firm, The Communications Co., the association is getting free advice from the firm on how to advance its cause.

Efforts to halt the dump appear dim, as the county continues to ready the 550-acre site. The county is working under pressure because of an order by the Maryland Health Department to close its overflowing landfill on Gude Drive in Rockville, nicknamed "Mount Trashmore."

County executive Charles W. Gilchrist has informed the council that he no longer will automatically send his staff to the council's weekly meetings on Laytonsville. He said the Laytonsville issue has been studied thoroughly for five years and suggested that further questions from citizens can be handled by mail and telephone.

"Simply, we won't participate in these week after week reconsiderations," Gilchrist said, adding that the meetings "are becoming rather a burden on the administration."

The county government's long-term solution to the trash problem is a $246 million facility that would burn about 1,400 tons of trash per day and generate the energy equivalent of 400,000 barrels of oil a year. The Solid Waste Energy Recovery Project is not scheduled to open until 1987 and is creating its own hot political opposition from residents who live near the proposed Shady Grove Road site.

The citizens opposing the incinerator project say the facility will produce toxic gases and heavy metals that will be a health hazard to nearby residents. Consultants for the county have said that the emissions will be slight.

The neighbors of Laytonsville, the site where the county expects to solve its immediate waste problem, do not care to have their rural surroundings used either, no matter how soon the incinerator is built. Under current plans, Laytonsville would continue to be used to store the incinerator's ashes.

"We have never been convinced that the landfill will be safe and that our groundwater wells will not be contaminated," complained Priscilla Benner, a Laytonsville resident who has become a regular at the county council's meetings.

Despite the impending opening of the landfill, Schoenke said he believes the association could stop the project with another $100,000.