Some ex-governors, die-hard defenders of states rights, would probably shudder at the thought, but the Southern Governors Association is planning to move its headquarters from Atlanta to Washington.

The move, some members say, will redefine the mission of the association, gathered here this week for its 48th annual meeting. It will also amount to a significant admission of the power of the federal government, even as the debate now starts on President Reagan's New Federalism.

"We can not just remain an organization for an exchange of views if we have no means of impacting on the decisions that affect us," said Virginia Gov. Charles S. Robb, who joined a majority of governors this morning in a straw vote approving the move.

But there are some Southerners who find it hard to accept Washington's power and prefer to see the governors association closer to home, back in its current office on Atlanta's Peach Tree Lane.

"It's just a question of whether you want the executive director to get up in the morning and read The Washington Post rather than The Atlanta Constitution," said North Carolina Gov. James B. Hunt, an opponent of the Washington move. "We should be setting our minds to what the states are doing, not what Washington is doing."

The move, expected to be formally ratified on Wednesday and begun next fall, has summoned up deep philosophic questions about the association's existence, the relationship of the states to the federal government, of the South to the North and a basic concern about symbolism.

"Some people seem to think that moving to Washington is inconsistent with virtue," said one gubernatorial aide, "They're afraid it will corrupt them."

Even those who are against the move are aware of the irony of its timing. "The New Federalism tugs both ways," said Florida Gov. Bob Graham, who this morning was the only governor to vote against the proposal. "It heightens the interest in what happens in Washington but it also puts more obligation on the states to manage what they've got. It's a matter of what people think are their priorities."

The Southern governors have talked about opening a Washington office for several years, but each time the proposal has failed for fearing of treading on the turf of the myriad groups--said to number more than 70--that represent the South's interests in energy, education and other matters.

But then last February, the Southern Growth Policy Board, which does economic research on the South, closed its Washington office, leaving the states and the governors without what some see as a single, centralized "Washington presence." The proposal before the governors would create an office in the nation's capital with three people and a budget of $125,000 a year.

Although most Southern states, including Virginia and Maryland, have their own Washington offices, the governors recently have believed themselves outgunned by the growing power of the Northeast-Midwest Coalition, a group of more than 200 congressmen representing 18 states and sister institute, that helps provides research on government programs and aid formulas for those regions .

It is the power of these groups, and the Coalition of Northeast Governors, that has made the South increasingly anxious about the need for a concerted Washington lobbying effort. Last year, a Sunbelt Council was formed to counter the influence of the Northeast-Midwest caucus.

"They the Northeast and Midwest have just discovered their problems. We've known ours since the Civil War," said one gubernatorial aide here. Historians also note that the SGA was founded as a lobbying group to seek repeal freight rates considered to discriminate against the South. From there, the organization has grown to include 19 governors from Delaware to the Virgin Islands.

David Merkowitz, director of communication at the Northeast-Midwest Coalition, applauded the South's effort but noted that the South may not need that much help. "They have been well served by their congressional delegations," he said, "which is, of course, part of the background for the founding of our organization."