Looking at this article, it seems that Bush is making great gains with his base, but his support among swing voters appears to be dwindling :

The National Annenberg Election Survey found that Bush led Democrat John Kerry by 54 percent to 36 percent on handling terrorism in polling from the end of the Republican convention to Sept. 12. The president was seen as a better commander in chief by 52 percent to 39 percent over Kerry.

On both measures, Bush’s standing was improved from early August after the senate convention. Other polls also have shown Bush growing stronger on various measures after the GOP convention.

But among swing voters, those who are undecided or say they might vote for another candidate, Bush appeared to lose some ground in the Annenberg survey and was no stronger than he was in August on the issues of fighting terrorism or being the better commander in chief.

Overall, the Annenberg study found the president received some bounce after the GOP convention on various measures, but that appeared to be declining through the week of polling. Bush’s job approval was in the mid-50s early in the period and declined to near 50 percent.

For swing voters, Bush’s job approval has declined from the 50s in mid-August to the mid-40s. That may be caused at least partially by Bush solidifying his support and removing some backers from the swing voters group.

But how do we explain Bush’s strength in the state and national polls? I dunno. Perhaps his base has more motivation to participate in the polls or something. The fact that his “bounce” has been slipping slowly away makes me think this thing will be dead even (or even leaning slightly toward Kerry) going into the debates.