They can take enforcement action. This could be bailiffs, or - if you are employed - getting an attachment of earnings order. Under this, money would have to be deducted from from pay by your employer and paid over direct to the Council. The amount deducted can be quite high. Ultimately, if the debt is not paid, they can ask magistrates to imprison you (this is very rare) and you still owe the money when you come out.
If you are genuinely unable to afford to pay it over 3 months you need to try and negotiate a longer period - you will have to provide them with a full income & expenditure statement to justify this. It might be best to do this through a free independent service such as the local CAB.
Are you paying money on credit cards, loans etc? If so, these are a lower priority than the council tax and you may have to let them get into arrears to clear the tax bill. Don't forget you must go on paying any current council tax instalments as well as paying off the arrears.