I imagine he'll do better than Dubya but don't expect another New Deal, especially with a milder recession than OTL. Keep in mind, Edwards won't have the massive congressional majorities of Obama. My best guess is that things will go something like this.
1. Edwards' economic policies are able to delay the crash and make it better than OTL, but won't prevent it entirely. He manages to get tougher regulation of the housing market, which means the bubble deflates rather than completely collapsing.
2. By 2007/08 economic growth begins to slow, but the economy doesn't start shrinking until 2009 or so. Despite the slowing economy Edwards manages to win reelection by a narrow margin, though not as narrow as TTL 2004.
3. As the economy enters recession in 2009, Edwards' approval ratings quickly falls as he struggles to get a stimulus through a closely divided Congress. While the recession isn't as bad as OTL, it's still pretty bad, while the housing bubble deflating instead of popping lessens the financial pain lots of people still lose their savings.
4. The 2010 midterms result in Republicans taking control of both houses of Congress. I talked more about how no Obama and a milder Great Recession could lead to a different American political scene
here.
5. While the economy begins to recover, Edwards remains unpopular, struggling with the new Republican Congress (though there's probably less obstruction than OTL) and after eight years voters are ready for a change, leading to the Republicans retaking the White House in 2012.
Again, this is just my speculation, I don't want Iwanh to feel like I'm writing his timeline for him.
