According to the wiki page for the 2004 election, here were the closest states:
1. Wisconsin, Kerry, 0.38%
* 2. Iowa, Bush, 0.67%
* 3. New Mexico, Bush, 0.79%
* 4. New Hampshire, Kerry, 1.37%
5. Ohio, Bush, 2.11%
6. Pennsylvania, Kerry, 2.50%
* 7. Nevada, Bush, 2.59%
* 8. Michigan, Kerry, 3.42%
* 9. Minnesota, Kerry, 3.48%
10. Oregon, Kerry, 4.16%
* 11. Colorado, Bush, 4.67%
So far only New Mexico, New Hampshire and Michigan have had primaries, and Michigan's has to be thrown out because Obama wasn't even on the ballot. Of the rest, Iowa, Nevada, Colorado, and Minnesota have held caucuses (though, Iowa and Nevada's were earlier than the others). Here's the breakdown in those states, excluding Michigan:
Iowa
Clinton 29%, Obama 38%
New Mexico
Clinton 49%, Obama 48%
New Hampshire
Clinton 39%, Obama 37%
Nevada
Clinton 51%, Obama 45%
Minnesota
Clinton 32%, Obama 67%
Colorado
Clinton 32%, Obama 67%
Based on this, it looks like it's actually Obama who has the advantage in the close states, by huge margins in Minnesota and Colorado, and a pretty sizeable one in Iowa. Clinton has a modest advantage in Nevada, and there rest are basically even.