Four times, President Barack Obama has stood in the well of the House of Representatives and delivered a State of the Union address—and four times, economic anxieties have largely overshadowed his efforts to push a broad agenda.

Tuesday night he makes his fifth such address—the State of the Union that will help define his second term. While the economy is improving and the mood in Washington is changing in significant ways, the story line isn't all that different: A broader Obama agenda is fighting to break out, but the economy...