There might come a day, A day may come, If a day comes to pass that...- these are all subjunctive and refer to possibilities as well as hypothetical situations and not things as they are.
There might come a day when I no longer enjoy throwing rocks at road signs, but that day is not today.
- this option is the least severe in terms of how it is heard, I would use it for just about anything,
A day may come that you can't find your house key, so let's hide one behind this rock just in case.
-this option sounds far more formal than the first as the word "may" is not particularly common in daily speech.
If a day comes to pass that you cannot walk, I will carry you.
-this option is the most severe and as a result I would only use it when the desire is to communicate the utmost sincerity.