No sooner had Arlington Republicans rid themselves of their longtime nemesis -- County Manager W. Vernon Ford -- than they encountered another source of trouble, this time from across the Potomac.

The more the Republicans in Washington succeed with their attack on the federal budget, the louder has been the cry from Arlington's service-conscious constituents.

The impact of those budget cuts has become a political liability for the Republican majority on the Arlington County Board, individuals linked to Reaganomics by both principle and party loyalty. And Democrats, priming for pivotal board elections in both 1982 and 1983 (the four-year terms are staggered so as to require elections every year), are making the most of the GOP's discomfort.

All of this comes at a time when the Arlington GOP should be enjoying its longest reign ever in a county once dominated by a Democratic coalition. After three years of unhappy confrontation, the Republicans succeeded in removing Ford, long considered an obstacle to their ambitions for a new conservative era in county government.

But in the aftermath of the storm surrounding Ford's dismissal in August, the ruling majority is showing signs of defensiveness. They are complaining that the Democrats have introduced a shrill new partisan tone into board debates, upsetting the once-genteel rules of Arlington politics.

"It's become much more political," Republican board member Dorothy Grotos said recently, "I've never seen this problem in the six years I've been on the board. I can't remember all this partisan business."

Democrats concede that they are pressing Republican weaknesses, getting ready for elections that could restore their majority on the board. "They're coming to the end of their assured majority," noted board member John Milliken, elected as a first-term Democrat in 1980.

Two of the three Republicans trace the increase in partisanship to Milliken, once an aide to former Rep. Joseph L. Fisher (D-Va.). While Milliken turns aside suggestions that board debates have become more political, he says that two of his innovations -- Democrat-sponsored town meetings and a newsletter -- may be making the Republicans nervous.

Other events have deepened the division on the board. Instead of marking a new beginning, the firing of Ford last August soon turned into a political drama, dragging on into the fall as the two sides wrangled over retirement benefits for Ford, a 22-year-veteran of county government.

"I don't know how much longer they expect us to be ladies and gentlemen," said Grotos. She was complaining of the Democrats' charge against Republican "backroom" tactics in the Ford firing. "When they keep making remarks like this, it does aggravate you," she said.

Milliken argues that the bickering over Ford's ouster was an aberration, since set aside in a show of togetherness over the search for a new county manager. But as the board now moves into a year when the demand for services exceeds available resources, old ideological differences are resurfacing with new intensity.

What Arlington is seeing is, to some extent, a local replay of the party differences at work in Congress over the last year. "The majority's effort is to hold down taxes, the minority's effort is to continue programs," said Republican board member Walter Frankland. "The definition of turf out there is very clear."

Republican board members say they're been willing to deal with the choices posed by the federal budget cuts. For instance, it was the three Republicans who recently resisted pleas from angry parents to restore federal money cut from the county's day-care inspection program.

"Certainly, in a community like Arlington, if we want more inspectors in day-care centers, why should we ask taxpayers all around the country to pay for them?" said Grotos, "It's high time for localities that want something to pay for it themselves."

What has angered Republicans most is their belief that Democrats are playing both sides against the middle in the budget debates, voting to keep programs without addressing the problem of where the money is to come from.

"The federal budget cuts are seen by Democrats as an opportunity to push their pet projects and programs," said Board Chairman Stephen Detwiler, a Republican. "On the one hand, they say we have tough decisions ahead of us and on the other, they're not willing to make them."

Detwiler, whose election to the board in 1978 tipped the majority into the Republican camp, sees the increased partisanship by Democrats as a sign of desperation. "You see votes become more politically based as an effort by the minority to maintain a power base which they've seen erode in recent years," he said, "As the majority's program begins to take hold, you see more and more desperate grasps by their side."

But so far, most evidence points to trouble for Republicans. On Nov. 3, incumbent board member Ellen Bozman, backed by both Democrats and Arlingtonians for a Better County, won reelection by a landslide, an indication to some that the old ABC-Democratic coalition is poised for a comeback.

Milliken attributes much of the vote to Bozman's personal popularity in the county. "But beyond that," he said, "there was some signal that people are concerned about the effect of budget changes on programs they care about."

Frankland is also still pondering the significance of last month's elections, which not only returned Bozman to the board but reelected Arlington's three Democratic legislators and swept in three Democrats to the state's top offices. "If more services is what the message of Mrs. Bozman's election was about, then maybe we have to readjust our sights," he said recently, "We'd have to give long and serious thought to what it is the people want."