In the closest thing left to a smoke-filled room in American politics, Arkansas Republicans will elect the first national convention delegates of the 1980 presidential campaign Saturday amid signs that Ronald Reagan's once iron-clad grip on the South is slipping.

Only 181 party members are eligible to participate in balloting for 12 delegates that will take place in four congressional district meetings. Understandably, the contest has not attracted widespread public attention.

But beneath the surface, four GOP hopefuls have waged a highly personal battle for months. "We've been wined and we've been dined by everybody," gushed party executive director Delia Combs. "I don't know how much more fun I can take."

Sen. Howard Baker, from neighboring Tennessee, and Reagan, who won two-thirds of the vote in the Arkansas primary four years ago, both claimed early leads.

But those "leads" have largely disappeared in recent weeks. And most party observers expect no single candidate to emerge as the clear-cut winner Saturday. Seven more delegates are to be elected at a statewide convention Feb. 16.

A separate Democratic primary is scheduled May 24.

"This thing is up for grabs," state GOP chairman A. Lynn Lowe said today. "It wouldn't surprise me that the candidate who finishes on top tomorrow gets three delegates and the one who finishes on the bottom gets two." t

George Bush, riding a wave of momentum from his upset victory in the Iowa precinct caucuses last week, is the single candidate who has the most to gain in Arkansas.

The Connecticut-bred Bush started late here as a largely unknown quantity, fearful that southern voters would turn their backs on him.

But Bush has spent more time campaigning in the Razorback State than any other candidate and he recruited popular Rep. John Paul Hammerschmidt into his camp. Normally cautious Hammerschmidt surprised party regulars by going whole hog for Bush. "He is our most electable choice nationally in November . . . let's join in helping nominate a winner for our party and the country," the congressman said in a letter mailed to state Republicans.

Bush and Baker are scheduled to appear at three of the four congressional district meetings Saturday, moves that are expected to improve their prospects. Reagan and former Texas governor John Connally are sending surrogates.

Reagan was an early favorite here as elsewhere in the South. In 1976, he slaughtered in the South. In 1976, he slaughtered then-president Gerald Ford in the primary, and ended up with 18 of the state's 27 delegates to the national convention in Kansas City.

Almost everyone concedes that if the state were holding a primary this year, the former California governor would again win handily.

However, Reagan's political operatives, once confident of a clear win, now downplay his chances. "We haven't spent the time or money here that the other three candidates have," said field director Paul Manaford.

Reagan's defeat in Iowa has hurt him here. "If we'd won in Iowa, everything would have a different complexion here," regional field director Rick Shelby said.

The Arkansas campaign, like the one in Iowa, has been highly personal, yet Reagan has treated both with remoteness. He spent three hours in Little Rock on Nov. 27 and hasn't been back.

Baker, Bush and Connally have made repeated visits. Baker has had Tennessee Gov. Lamar Alexander, former governor Winfred Dunn and Tennessee congressman Robert Beard campaign for him. Connally created the biggest sensation of the campaign by inviting some 250 GOP decision-makers to an all-expense-paid weekend at an Arkansas resort. It was a lavish event, marred only by the heart attack of one would-be delegate.

The tiny Arkansas Republican Party has loved the attention. "In other years, the closest we've gotten to the candidates is to have them fly over our state on their way somewhere else," said state chairman Lowe. "Now our county committee members are getting letters and phone calls from all of the candidates.Some candidates are even having their brothers and sisters knock at doors."

Some county chairmen complained of getting as many as a dozen calls a week from various campaigns. Today Barbara Bush was making one last round of calls from Little Rock. "Hi, this is Barbara Bush, George Bush's wife," she said. "Bet you know why I am calling. I'm hoping I can answer any questions and I hope I can talk you into voting for his delegates tomorrow."

Spokesmen for all of the campaigns predict that Saturday's vote will be split. In addition, some well-known party members are running as uncommitted delegates in the district meetings and in the state convention Feb. 16.

"I'd love to say we're gotta win a minority when it's all through," said Phyllis Kincannon, Baker's Arkansas campaign manager. "But I don't think anyone is going to get a clear-cut victory."