Is there any way I can get an extension for my eviction?

My family has lived in our apartment for 6 years and have always paid our rent on time. Recently, my father became very sick and is unable to work. He was hospitalized for a month. We were short on the rent but management accepted partial payment and verbally agreed to a payment plan. Days later, I received a pay rent or quit notice on my door. I went to the management and asked if I was being evicted. She said no, not to worry about it. I assured her I would make a payment as soon as possible. About a week later (on a Saturday), I was served an eviction notice. My check came in days later. I went to pay rent in full and my payment wasn't accepted and was advised to call their attorney. I called the attorney and asked if there was anything I could do. They told me they would contact their client and get back to me the next day. They never called me back. I called in the next day. They spoke to the supervisor and informed me that they were unwilling to work with me. I asked them if they’d spoken with the owner. They said they spoke to the supervisor and there was nothing I could do. Two weeks later, June 2 2016, I received a sheriffs notice on my door to be out by June 8. I called for an extension until the end of the month. The sheriff told me to call the attorney. The attorney said to call the management. Manager said told me to call the attorney. No one wants to help me. I explained to them that I have 1 year old twin boys, I'm 7 months pregnant, my father is in the final stage of renal disease, my younger sister and my husband we have no place to go and need at least until the end of the month to find a place. I've explained to them that I can pay them rent to allow us to stay for the rest of the month, and I will hand over the keys and sign whatever papers need to be signed. No one is listening to me. I feel my family is being personally attacked. We’ve never had any problems with paying our rent. The one month we were unable to pay in full were being thrown out on the streets.