With the limited information available to the general public, it is difficult to assess the issues in play. However given the degree of hostility evident in the streets of Egypt to the Morsi regime and the clear decline in the economic condition of the populace, the rational course would be for Morsi to seek an accommodation with the military and come to an agreement on a way of going forward. This could include an agreement to hold both parliamentary and presidential elections within a year.
Unfortunately, compromise is an idea in short supply in the region. Loss of public standing is more feared than removal by force. Indignant righteousness is a better presentation than being seen to take less than you are entitled to.
“Should” is a tricky word in the English language. Morsi will not resign and will suffer removal rather than damage the image of the Moslem Brotherhood in the eyes of its followers. A new grievance is for them a new cause to rally their followers in the times to come.