What can I do if our apartment manager gave us a 3 day to pay or quit notice because we owe half the rent?

You are wrong as to the obligation to pay rent. A verbal contract to rent/lease is the same as a written one; why would you be entitled to live there if you did not have to pay any rent? However, the owner [not the manager] appears to be in breach of the contract because you rented on the belief that the garage roof had no defects so either they need to repair it within a reasonable period of time [which has passed] or you can spend up to one months rent to have it repaired after giving them notice that you will be doing so. But realize that anytime you get into an argument with the landlord, they are going to look less favorably on you as a tenant. Go over the manager's head and speak to the landlord directly about the defect and that is why you have not paid the full rent. But legally, you are not able to deduce the repair costs until you have given notice you will and you have actually spent the money, so the landlord is within his rights to give you a 3 day notice and in court you will have to raise a Green v. Superior Court [look case upon on internet] argument that the rent should be lower than the agreed to price so you do not owe as much as the landlord claims [but that may not prevent the eviction, just lower the amount you owe]. ?It probably is worthwhile to contact a local tenant's attorney for a free conference to see what can be done. Normally, in California, you just have 5 days to file an answer to an unlawful detainer suit that is filed against you after the 3 day notice time to cure runs out.