It could be a problem.
The concern with things like this is that they will cause an intestinal blockage. This is more common in small dogs than in large dogs.
You have two choices:
You can see the vet within one hour of the occurance and have the vet retrieve the tinsel before it has an opportunity to cause a blockage.
Or you can wait and see what comes out - literally. Some dogs will pass things like this on their own but a good number cannot. If you see vomiting, lethargy or diarrhea, you should rush to your vet right away.
Let me know if you still have questions.