If you stay past the terms of your lease, you will be a a month to month, under the same terms and provisions as the lease. Even if your landlord tried to evict you, it is unlikely you will be forced out before May. Keep looking for a new place t live.
This is in Skokie, not Chicago, and so there is no requirement that your landlord give you written notice of intent to not renew a lease that has a specified end date (3-31-2013). In other words, if the lease says it ends 3-31-2013, then that is when it ends, and neither party has to give the other party any notice of intent to not renew. That is, unless your lease says the landlord or tenant must give a written notice of X days to not renew.
Without the landlord's permission, you are a hold over tenant if you stay past the lease expiration. If the landlord accepts your next monthly rent payment, then as the other attorney mentioned, it could just become a month to month rental and there will be no problem. But, if the landlord does not accept your rent the month after your lease ends, they are entitled to refuse it and serve you with a written notice to vacate. If you do not move out after receipt of that notice, in WRITING, you could be considered "willfully holding over" and liable to the landlord for double the monthly rent for your time spent there after the lease ended. That is important to be aware of.
The law about willful holding over and the double-rent penalty appear in the link below, or are found anywhere that publishes the Illinois Compiled Statutes at section 735 ILCS 5/9-202
This information is general and does not constitute legal advice, or create an attorney client relationship.
I agree. While the eviction process will take a few months, it is likely to result in a money judgment against you. Maybe you can try to renegotiate with the landlord. Good Luck.
I agree with the previous answer; try to negotiate a 1-2 month extension with the landlord. The two of you can execute a simple rider to your existing lease stating that there is an extension and any new terms (such as an increase in rent) that will be in place for the length of the extension. Good luck.