Talk to the Landlord
This is something that you should have done before but still can be done after the notice has been served. You can ask him or her for some extra time and explain your circumstances. Most people are willing to listen and consider. Communication in this regard must be crystal clear and do not leave any ambiguity in your request.
If you are able to convince your landlord, you can have a special settlement put in place. Try to pay your rent partially at least when you are talking to him or her and let them know that by when you can pay off the balance. It is quite likely that if they see that you can pay the rent on time in future that they may take the notice back.
File Counter Claim
If the above mentioned method does not work, you can resort to a counter claim. This can be regarding a breach in the terms of agreement by the landlord such as maintenance not being done as per the decided schedule. You can demonstrate that the landlord has been negligent of your needs and has not worked as per the agreement. This may get the eviction notice annulled. Make sure that the claim is not a fake one.
Request a Stay
This is a toughie but worth a try. Explain to the judge that although you have been unable to pay your rent, you have every intention to do that. Explain the gravity of your circumstances and what has prevented you from meeting your rental obligations. The bad economic conditions plea generally does not work but can in some cases. A good rent payment history can help.