Trygve Throntveit is assistant director of undergraduate studies in history at Harvard University; he is currently at work on “Power without Victory: Woodrow Wilson and the American Internationalist Experiment.”

In evaluating President Barack Obama’s legislative record, historically inclined commentators frequently compare his first term to the early years of Franklin Delano Roosevelt’s New Deal. When it comes to winning re-election, however, the commentators — and Obama — might learn something from the only Democrat besides F.D.R. to win multiple elections in the 20th century on reform platforms: Woodrow Wilson.

Obama won in 2008 largely because he promised a new way of doing things in Washington: less partisan and ideological, more cooperative and deliberative. His recent turn to the left might energize the Democratic base, but it is unclear how it will play among the swing voters who put him in office and remain crucial to his re-election. That’s where Wilson comes in. Few presidents have wooed swing voters as successfully as Wilson: In 1912 he won liberal Republican votes from both William Howard Taft and Teddy Roosevelt when the latter bolted to form the Progressive Party, and in 1916 he added former T.R. Progressives and even socialists to his coalition to win a close race against the formerly liberal, increasingly conservative — in other words, eerily Romneyesque — Charles Evans Hughes. In that race Wilson, like Obama, signaled a clear turn leftward, but that alone did not win him re-election. Instead, Wilson won by doing something Obama has not: staying on message, which for him meant staying on method....