By the power to persuade Richard Neustadt means that a president must have what?

The president is only one man and needs others' assistance to get things done. He must bargain and persuade others that what he wants is in their best interest. President Truman once said of President Eisenhower, "He'll sit there all day saying do this, do that, and nothing will happen... He'll find it very frustrating." This refers to the president as an "office commander", in which the president must balance differing interests.

Just because the president wants something done does not mean that the others, who also possess the power and authority, will carry out his wishes.

The presidents advantages are checked by the advantages of others. Relationships will pull in both directions. These are relationships of mutual dependence. The president depends upon the people that he would persuade; he has to deal with their need or fear of them. He must convince people that his policy will benefit them as well.