I recently painted my apartment in Los Angeles CA where I have lived for six years without permission from my landlord and in violation of my lease. I accept full responsiblilty for this and realize I am in violation of my agreement. There were no other changes to the premesis other than the color of paint on the walls. I have been issued a "Notice to Cure" and given a completion date. If I do not comply, management will not renew my lease at the end of next month. Fine. I went out and bought a condo.
What is my responsibility to this landlord as far as repainting before I move out and if I do not, how much of my deposit are they entitled to keep for this "repair".

You should consult the terms of your lease. However, if you do not re-paint, the landlord will indeed take money out of your deposit to cover the cost. The landlord should only take the exact amount it costs to re-paint out of your deposit, unless there are other fees listed in the lease. That doesn't mean they won't take more, at which point you would have to contest it, probably in court.

As said above they can and most likely will take the money to re-paint out of your deposit. And the cost will depend entirely on who they hire to re-paint. You will not, unfortunately, be able to have a say in who they get to re-paint. So it could be very costly. It may cost less for you to re-paint yourself. That way you know it will only cost the price of paint and not the paint and labor you will be charged.

It may be more serious than either simply repainting or losing a portion of your deposit. If your lease is terminated prematurely by your admitted breach of contract, you can be held liable for the remaining months of rent on the lease or, if on a month-to-month, rent for each month up to the time in which the landlord obtains a writ of restitution for recovery of the property.

In short, it's probably much cheaper to repaint the walls white.