How can I identify foreign object on my dog's feces?

My dog (Jack Russell mix, 1 1/2 years old) started vomitting on Wed. It was only once a day (in the afternoon) and he was still eating and eliminating normally. After the third day of the vomit, we saw our vet. An x-ray revealed that he had eaten something that he couldn't digest. Luckily, it had moved from the stomach into the colon. The vet expected him to pass the object within a day or so (this was on Saturday morning). Since I gave him plenty of fluids, his feces over the weekend were runny. Monday morning he had a very solid, bigger than usual poop but I didn't notice anything in it. Should I still be expecting something to pass? Will it be noticeable in the feces? I have been going thru them with a stick.