Einstein thought this may happen. The field concept is central to Einstein's approach to physics. It suggests we can model physics by looking at what happens at an arbitrarily small region of space. What happens at a point in space is completely determined by the immediate region of that point. Distant objects can only have an effect through the fields they generate and that propagate through space.
Relativity implies continuity.
No matter how small a region we select the same rules apply. As we move to smaller time and distance scales the complexity of what can be observed according to increases without limit. This alone suggest that at a sufficiently small scale will fail. There seems to be no way to reconcile these two theories within the existing framework of either. Perhaps it is such considerations that led Einstein to suspect that ultimately physics cannot be based on continuous structures.