A five-member majority of the Montgomery County Council, declaring that Montgomery does not have to follow President Reagan's lead, yesterday rejected a proposal that would have trimmed next year's budget by cutting the county's share of employe health benefits and eliminating county employes' annual merit raises.

The council did agree to take up the issue of increasing the amusement tax on video games from 7 to 10 percent. The so-called "Pac Man" tax would raise about $500,000 at a time when the county government is facing a revenue shortfall in fiscal 1984 that could reach $20 million.

By voting 5 to 2 against considering the salary proposal, the council members avoided for now one of the county government's most pressing fiscal problems and thorniest political dilemmas: how to control the spiraling costs of employe compensation in a county where the professional public sector is considered close to sacrosanct. Montgomery politicians, including County Executive Charles W. Gilchrist, have run into political trouble and stiff opposition in the past by proposing changes in the county's strict civil service protections.

That proud county tradition is threatened by some disturbing fiscal projections, however. A task force of the Greater Washington Research Center, in its December report, concluded that Montgomery's fringe benefit package to employes would rise by 104 percent from 1982 to 1987, while wages would increase by 37 percent, unless the government took action to control costs.

The council has established a task force to study employe compensation. But Council President David L. Scull, citing what he called the urgency of the problem, proposed asking the county executive to eliminate the automatic 2 percent merit raise county employes now receive. Scull also proposed making employes and the county government share equally in the cost of providing group health and life insurance benefits. Currently the county pays 83 percent of an employe's health care package.

Acknowledging that Montgomery is still "a lucky island of relative prosperity," Scull reminded his colleagues that other government workers were taking pay freezes. "The federal workers, and there are many in our area, will get zero if President Reagan's legislation is passed by Congress," he said. "State workers are also looking at zero pay raises ."

But Scull could not even muster the majority votes needed to introduce his bill, usually a perfunctory matter. "I think what Mr. Reagan and others are doing downtown should not be our guideline," said President Pro Tem Michael Gudis, a Scull ally on the council.