On Saturday, the military warned of "disastrous consequences" if the crisis is not resolved.
The cancellation of the army's meeting was likely made under pressure from Morsi, who has been adamant since he took office that the military must stick to its core mission, such as protecting borders. Although Morsi appointed army chief el-Sissi, he is not seen as tightly controlled by the president.
"The military is boiling. The military doesn't live in isolation from the street and what is happening there. We have judges on strike, a constitutional court under siege and a media city under siege," said retired army general and military analyst Hossam Sweilam.
"We have large sectors of Egyptians rejecting the referendum and we have so many ways to postpone it. But the stubborn leadership is insisting on going forward with the process. All this is reflected on the armed forces."
"The patience of the officers is not guaranteed to remain the same forever," said Sweilam, who is widely thought to be close to the military.
The vote for half a million eligible expatriates overseas could give hints at which direction the referendum is going. Egyptian expatriates in the Gulf are known to lean toward Islamists while others in Europe, North America and Australia, among them a large number of Christian migrants, lean more toward liberals.
In the Egyptian embassy in Sanaa, Yemen, a handful of voters showed up after the vote started at 8:00 a.m. local time. Mohammed Abdullah, a physician, said he voted yes because he wants stability, and any changes could be made later.
"We can make whatever amendments we want but we have to get through this and return to normalcy," he said.