1. A broker will allow day trade margins when the electronic markets are open. For ES this is from 3:30 pm to 3:15 pm central. If you hold a position past 3:15 you will be required to have in your account enough equity to meet the exchange margin - for ES that s $6,000.
2. It is at the discretion of the broker and firm to liquidate or not. I have had margin calls from time to time and have not had my position liquidated.
3. It will also matter what day you carry over. Is it Friday afternoon? Your broker might not want the risk of carrying the trade over the weekend. During the week M-T you are only on full margins from 3:15 to 3:30 central.