According to the Stoics, in order to be able to better deal with the possibility of a nightmare scenario, you should imagine it in detail.
Hold on to your socks.
SCENARIO:
Financially, your back is against a wall. If you lower your price at all, doing this job would lose its purpose, as you would need to find and sell another one at the same time to get the money you need. Likewise, you cannot really afford to not get this job now, because it’s unlikely you will find another before the looming deadline.
Worse, you are probably not hiding these facts very well, and the client suspects you are desperate.
OPTIONS:
First of all, there’s very little negotiating you can do, there’s not much room for it.
Asking for fairness, pleading, or playing for sympathy from somebody who can lose out if they give in to their better nature is unlikely to do you much good. It’s a “moral victory play” you can’t really afford.
Raising your tone, responding to an insulting price by raising your initial price, or playing hard-to-get usually backfires, and then forces you into a humiliating climb-back. It’s a “macho play” that is too risky by half.
I advise putting 100% of your energy into defending about 10% of your time as a “previous commitment”. This is done to create a potential for later leverage by doing better-paid side jobs, and one day be able to exit the current job and survive.