A leading Republican pollster yesterday said President Reagan's approval rating has leveled off at about 45 percent after a steep slide earlier this year, and that he doesn't expect that Reagan will ever drop as far in the polls as Jimmy Carter did.

Robert Teeter, president of Market Opinion Research Co., said the leveling off indicates that Reagan has "sustaining" support that will prevent his approval rating from dropping below 33 percent. By contrast, Carter's approval rating hit a low of 21 percent in July, 1980.

Teeter told reporters that Reagan's rating fell in January and February largely because of questions about the fairness of his economic policies and a shift in opinion about his presidency among southern Democrats who had supported his election.

In February, Reagan's approval rating in the Washington Post-ABC News poll was 48 percent; 46 percent disapproved of the way he was handling the presidency. In the most recent Post-ABC poll, taken in May, 46 percent approved and 45 percent disapproved.

By comparison, Lyndon B. Johnson had an approval rating of 67 percent in a Gallup Poll taken at a similar time in his presidency, Richard M. Nixon had 66 percent, Gerald R. Ford 45 percent and Carter 43 percent.

Teeter said he expects Reagan's popularity to increase slightly as a result of his recent European trip, and said the economy will dominate the fall elections.

He gave a rather gloomy assessment of Republican election prospects. For the GOP to have even a "decent year," he said, unemployment and interest rates must drop so that candidates "can make the case that the economy is getting better."

Teeter defined a "decent year" as one in which Republicans might lose 10 to 12 congressional seats and two or three governorships while gaining one or two Senate seats.

The GOP has made some progress, Teeter said. In March he said his polls showed the public, by 60 percent to 15 percent, believed inflation was getting worse. That margin is now 46 percent to 29 percent, he said.