The Rev. Jesse Jackson is trying to stir unregistered eligible black voters in the South to get registered, and he is stirring up southern conservatives mightily in the process as well. Some sound downright alarmed.

Sen. John P. East (R-N.C.) has sent a letter to members of the National Congressional Club, a political arm of his colleague, Jesse Helms (R-N.C.), who is up for reelection next year.

The letter said that the latest Gallup Poll shows that "liberal Walter Mondale would beat President Reagan by 6 points" and that "ultra-Liberal John Glenn . . . would trounce President Reagan by 17 points!

"And that'e before Jesse Jackson registers 2 million more 'straight ticket,' anti-Reagan, minority voters. That's the next step in the liberals' battle plan!"

East goes on to warn that it would also defeat conservative senators such as Helms, John G. Tower (R-Tex.) and Strom Thurmond (R-S.C.) "and give Ted Kennedy control of the United States Senate!" Because "time is running out for us and Jesse Jackson's liberal army is growing," East urges the Congressional Club members to send money for the club's "Campaign to Register a Conservative Majority."

He winds up: "We need to register more conservatives--young or old, rich or poor, black or white."