There's no evidence that shows or correspondences that suggest the web-like pattern on the dollar bill are supposed to be spider webs; the pattern may simply be used for aesthetic value. However, some people claim to see a spider on the dollar bill among other things.
The tiny spider on the dollar bill appears on the upper-left part of the shield-shaped object surrounding the "1" on the upper-right portion of the bill. However, some people claim to see an owl instead of a spider, making the claim a bit dubious. The detailed, ornate look of the dollar bill and many instances of symbolism fuel a number of conspiracy theories about hidden messages on the dollar bill.