Public prestige means the judgment of insiders about how the public will react to their own reactions to the president. Public figures count on members of the larger public to accomplish many thing they care about. The politicians, in particular, care about getting elected. So they care about how the public will assess their interaction with the president.
Prestige isn't as simple as a raw measure of popularity. Much of the public is usually inattentive, so the esteem in which they hold the president has little consequence. The president's prestige will also vary in different constituencies, and even in regard to different issues.
The president's prestige also affects him more immediately, because he often wants things directly from members of the public, whether votes for himself and his allies or private actions that further his policies (for example, union members' cooperation with Truman's seizure of the steel mills).
Like his professional reputation, a president's public prestige does not guarantee that he will get his way, but it can gain him leeway.
A president's personality comprises a large, but mostly static component of his prestige. The more variable element to his prestige comes from changes in the public image of the presidency, which is to say changes in what the public wants the president to be. These changes are driven by events that affect members of the public, especially negatively, like economic trouble, military conflict, and social unrest. Since presidents have limited influence on such happenings, their prestige depends on their success in managing the hopes of the public. They must teach the public to see their role in a favorable light. But this instruction takes place under four constraints: (1) the public is chronically inattentive, (2) when they are attentive, it is in the context of pressing events not likely to be of the president's choosing, (3) deeds will influence public perception more than words, and (4) how the public understands the president will be influenced by the context of what he has previously done and said. In other words, both events and his own record will compete with the president's attempts to shape public perceptions.
A president's choices of action affect his bargaining power, his professional reputation, and his prestige. Since so much depends upon his choices, a key question is how a president husbands and preserves his latitude to make choices.
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