Hate that mojo is into mischief. String or linear foreign bodies are a real worry since they can slip into the intestines and then the intestines can "grab" the string at multiple points during normal peristaltic contractions and end up having a tug of war type situation. String can easily saw it's way through the intestine resulting in perforation. Further, the intestines can contract and end up walking it's way up the string, causing the intestines to bunch and even engulf other stretches of intestine causing an intussuception. These are all potentially life threatening issues requiring surgery. However, many dogs have eaten strings and ribbons and gone on to pass them without problem. Not every string requires surgical intervention. I do think it's wise to consider getting a baseline x-ray of the abdomen to look for classic string foreign body intestinal pleating. If this is found, then preemptive surgery might save a whole lot of stress and possibly mojo's life. If the abdomen looks good, and the vet can add their skills of feeling the gut to your own, then we may be able to wait it out. Taking it day by day requires that the dog is not vomiting, and ideally should be eating. If we can keep mojo eating, then the food will help improve intestinal transit of the string, and it all might poop out in the end. If he stops eating, or worse if he starts vomiting, another x-ray and likely surgery will be the end result.
If healthy, feed regular or even increased meals to help bulk things through. Consider an x-ray as a base line to help your vet make the frustrating decision on surgery based on subtle changes from one x-ray to the next. It is unlikely the string itself will be visible so your vet will be using experience interpreting changes over time.
If vomiting or not eating, strongly consider a recheck ASAP and be prepared for possible surgery. Hope this helps.