If Georgia Gov. George Busbee challenges Sen. Herman E. Talmadge (D-Ga.) for his seat in the Senate next year, Busbee will beat him by more than 2 to 1, according to a current public opinion poll of Georgia voters.

The poll results could signal an end to the decades-long undisputed political influence of the Talmadge family in Georgia and national politics. In addition to his Senate service, which began in 1957, Talmadge was governor of Georgia, as was his father before him.

The poll, commissioned by WAGA-TV in Atlanta, was conducted Feb. 13-16 by Darden Research Corp. of Atlanta. The scientifically based sampling included telephone interviews with 500 adults in 55 Georgia communities.

The findings also indicated that former federal budget director Bert Lance would have very little chance of unseating Talmadge, whose term expires in January 1981.

When asked, "If George Busbee was to run against Herman Talmadge for U.S. senator in 1980, who would you lean toward?" the registered voters responding to the question divided as 66 percent for Busbee, 28 percent for Talmadge and 6 percent undecided.

In the poll match between the 65-year-old senator and Lance, 59 percent chose Talmadge, 24 percent chose Lance and 17 percent were undecided.

The sampling also measured a prospective race between Talmadge and Atlanta Mayor Maynard Jackson, who unsuccessfully challenged Talmadge in 1968.

The results of the poll were Talmadge, 58 percent, Jackson, 29 percent, and undecided, 13 percent.

The poll also showed that Georgians continue to give President Carter a mediocre rating in the performance of his duties.

A total of 44 percent of the respondents gave Carter a "very good" or "good" rating. Forty percent judged him as doing a "fari" job, while 15 percent described his job-handling as "poor" or "very poor." One percent were undecided.

However, Georgians continued to favor Carter against potential challenges by Sens. Edward M. Kennedy (D-Mass.), and Howard H. Baker Jr. (R-Tenn.), and by former Treasury secretary John B. Connally and former president Gerald R. Ford, both Republicans.