Republicans, who hold only 16 governorships, are optimistic about picking up several this year. Recent polls give them hope in two southern gubernatorial races, Texas and South Carolina.

In the most recent Texas Poll, taken from Jan. 24 to Feb. 6, 9 percent rate Gov. Mark W. White Jr.'s job performance as excellent and 33 percent rate it good. He is rated as fair by 30 percent and poor by 23 percent, a surprising overall unfavorable rating of 53 percent. Said Texas pollster George Shipley: "White is in deep trouble."

In match-ups against potential Republican challengers, White runs neck and neck against former governor William Clements, whom he defeated in a bitter race in 1982, leading him by a statistically insignificant 43 to 41 percent with 16 percent undecided. White fares better against two other Republicans, who have low name recognition. He leads former representative Kent Hance by 46 to 33 percent with 20 percent undecided, and Rep. Tom Loeffler by 47 to 27 percent with 27 percent undecided.

In South Carolina, a poll taken from Jan. 27 to Feb. 4 for The (Columbia) State shows Lt. Gov. Mike Daniel (D) leading Rep. Carroll A. Campbell Jr. (R) by 46 to 41 percent, which is within the margin of error, with 13 percent undecided. The key could be independent voters, of whom about 19 percent are undecided.