Who has the political edge -- challenger or incumbent?

There is a myth that needs to be exploded - that it is becoming nearly impossible for presidents to succeed themselves. The theory, expressed repeatedly by political pundits these days, goes like this: A president comes into office with a certain amount of popularity. Then, because the problems he deals with in these difficult times are so immense, the president is unable to solve them. His popularity wanes, and voters give him only one term.

Supporters of this one-term thesis usually add about here: ''Eisenhower was our last two-term President.'' That's only partly true. Nixon was elected twice; he just wasn't able to finish the course. Further, it isn't fair to include Kennedy in this short-term argument. Also, Truman and Johnson didn't go to the electorate more than once.

Sure, Messrs. Ford and Carter were short-termers. But Ford almost got elected. And his pardoning of Nixon may have been the special circumstance that prevented it. And Carter? He did, indeed, lose out because of the public perception that he simply wasn't up to the job. But it can be argued that Carter was not the typical President responding to a typical problem.

A much more persuasive argument - and one that was long propounded by political experts with great certainty in their voices, until lately - is that an incumbent president has a great advantage when it comes to getting re-elected. Further, it will be Reagan's advantage - if he wants to seize it.

Senate minority leader Robert Byrd's words about his prospects of running for president in 1984 bear on this thesis of presidential advantage. Asked by reporters the other morning whether he might not seek the Democratic nomination, the veteran senator said, ''Not a chance in the world.''

Senator Byrd then went on to cite the extremely difficult path that a challenger must take to gain the nomination:

''You know,'' he said, ''our system has changed so that to get the nomination of a party, one has to live out of the suitcase . . . (for) two or three years in advance.

''You have to organize in the various states and engage in the various primaries, . . . and to do that would mean someone like myself would have to leave the Senate.''

Several Democrats, some of whom, like Sens. Ernest F. Hollings, Alan Cranston , John Glenn, and Gary Hart, do have obligations to their constituencies, are already deeply involved in the time-consuming task of trying to make it to the White House.

They are all trying hard to become more visible. They draw a small audience here, get on a local talk show there. And when they announce their candidacy, they get a few seconds on the evening TV shows - if they are fortunate.

Meanwhile, look what a president can do. Mr. Reagan calls an evening TV press conference and draws 60 million viewers. His secretary of state goes to China, and everything he does is closely followed by the American public through countless newspaper, TV, and radio stories. His vice-president goes to Europe - and once again the administration gets all kinds of media attention for what George Bush is doing and saying.

Certainly, all that visibility can work the other way, too. If a president and his administration go sour - well the negative image can be overpowering. Lyndon Johnson learned about this. So did Richard Nixon.

But even if a president is unable to do better than show he is making a little progress in dealing with his problems - as Reagan is today - his visibility will remain an advantage.

Another way of putting it is that Reagan's incumbency will likely be very much to his advantage in 1984 - not the other way around.

Senator Byrd, at breakfast, did have an opportunity to get a little visibility, a little ''ink'' as it used to be called.

Would you assess the performance of the President at midterm?

Well, I'd say that in forging policy there has been a great deal of confusion. Other countries just don't know where we stand. We haven't consulted with them. I'd criticized Mr. Carter for that - or, at least, suggested that there be more consultation with our allies before we move in certain directions. So I would say in foreign affairs the President would probably not get too good a report card.

How about Reagan's rating on domestic matters?

I would say the sad state of the economy - the fact that more than 11 million Americans are out of jobs, all these foreclosures of homes and farms - means that the President should get pretty low marks.

At the same time the President has gotten just about everything he's asked for. He asked for the tax cut; and then in order to rectify the damage that tax cut obviously wrought upon the country by way of the big deficit, he came back and asked for tax increases. We passed a $99 billion tax increase last year, together with a second tax increase, on gasoline. So I wouldn't give the administration very high marks.