Bob Davis of the Wall Street Journal is skeptical of Obama's free trade credentials:
Since at least John F. Kennedy, presidential candidates have campaigned as tough on trade and then governed as free traders. Some business leaders are expecting the same if Barack Obama makes it to the White House.
Don't count on it.
Sen. Obama, the Democratic party frontrunner, and his rival, Sen. Hillary Clinton, have expressed some support for trade liberalization during their careers, as public opinion and congressional politics have shifted markedly against free trade. A coalition of anti-free trade activists and labor unions also has used the long primary season to wring commitments from the two candidates on an astonishingly detailed list of trade issues, making it hard for them to reverse course.
More at the link.
I suppose this issue depends in part on what you mean by "govern as a free trader." Obama might look more like Bill Clinton than like George Bush on trade issues, but he's clearly no Ross Perot.