The play would have ended differently for both Caesar and Brutus. Caesar would not have died on March 15 (the Ides of March) but eventually the plot would have played out...plans evolve and change for a reason. Plan B or C or D would have been put into place.
Brutus, however, may not have been made the scapegoat of the conspirators on another day. The blood spilled anywhere else but the Senate floor may have been a turn for the better for him and his ability to salvage his reputation and the reason he went along with the plot in the first place.
The assassination wouldn't have taken place that day, but it would have happened eventually. Caesar had too many enemies who were envious of his power. One catalyst of the plot that Shakespeare pays little attention to is Caesar's relationship with Cleopatra. She was in Rome at the time of the murder because Caesar wanted to acknowledge their son as his heir. Rome had a mighty army, but Egypt fed the world. With both under his control, Caesar would have been unstoppable. Someone would have killed him.
Do you think he would have stayed because of his wife? Yes, he seems to have agreed to her pleas to hand around the house for the rest of the morning, but how long do you think that would have lasted? I believe that the lure of becoming king that day would have brought him out of the house sooner or later. Listening to Calpurnia may have delayed it for a few minutes or even a few hours, but it was going to happen anyway.
Julius Caesar was about to give in to Calpurnia's pleas when Decius quickly thinks on his feet. He reinterprets the dream to make it seem like a positive omen, and not the negative one Calpurnia feared. Even the priests said the dream was a bad omen when they were consulted as "a second opinion"; they cut open an animal to find that it had no heart. Caesar was very close to staying home before Decius played on his ego and convinced him that giving in to a woman's fancies would make him seem weak in the eyes of the people of Rome. Had Caesar yielded at that time, though, I am sure that the conspirators must have had a back-up plan ready. Since Cassius was so determined to assassinate Caesar, he would not have allowed a missed appointment at the Senate house to stop him.