President Carter would have significant difficulty carrying his home state of Georgia if he runs for reelection in 1980, according to a survey of current public opinion.

In 1975 and 1976, Georgians provided the financial and political foundation for Carter's stellar rise, and gave him 67 percent of their votes in the November 1976 election.

Now, according to the poll, only 41 percent say they are willing to vote for him in 1980.

The telephone poll of 500 adults in 55 localities around the state was commissioned by The Atlanta Constitution and conducted Aug. 23-28 by Darden Research Corp. Election results have shown previous polls by the 10-year-old Atlanta firm to be very accurate.

The same 500 people were asked whether they would vote for Sen. Herman Talmadge if he runs for re-election in 1980, despite investigations of his financial affairs. Of those who knew about the Democrat's problems with campaign and office finances, 52 percent said "yes," 32 percent said "no" and 16 percent were undecided.

Among Carter's 1976 voters, the erosion was remarkable. Of each group of 100 Georgians who cast 1976 ballots for him, 54 are willing to do so again.

In a June 1978 survey of 501 adults, Darden Research asked whether Carter or his successor, George Busbee, was the better govenor of Georgia.

The answers: 45 percent said Busbee, 17 percent said Carter, 15 percent said the two men were equal ability, and 23 percent were undecided.