Any idea how long ago he may have eaten it?What breed is he?
Thanks for answering my questions.
At this point, I think the best thing to do would be to get him to vomit the shoestring if we can. The way to make that happen is pretty easy and instructions can be found here: http://www.petplace.com/dogs/how-to-induce-vomiting-emesis-in-dogs/page1.aspx (when the pop up window appears on this site, you don't have to register, just go ahead and hit the 'close window' link at the bottom of the window).
The reason I want you to do that is because items like shoestrings or strings off toys tend to have one part heading through the digestive tract and the other part still in the abdomen. When that happens, the peristalsis (the spasms that the intestines to do push material through) can actually cause the strings to saw through the intestines, which then tear and can be fatal to the dog.
If this were my dog, I'd see if I could get her to vomit the string. If you can't, then I would seriously consider having her seen by an emergency vet tonight (if your vet is already closed)...just to be on the safe side.
I hope this helps.