When you begin all your planning for salary negotiation, one of the numbers you will need to calculate is the lowest overall compensation you are willing to accept (LCWTA) for a given position. You won't share this number; for example, this should NEVER be used as the bottom of a salary range you offer. (Which, by the way, you should avoid offering a range whenever possible).
Your LCWTA is a number you calculate for yourself, and yourself only. If your employer can't even meet this number, it's really important to be able to politely thank them for the opportunity and walk away.
Well, for one thing - you're setting yourself up for failure if you walk into a position where your market value is already severely compromised, or you're being underpaid. You likely won't be happy, and will potentially experience a lot of anxiety if your pay is too low to meet your basic needs.
Second, if you counter an offer with an indication that you're walking away from the negotiation, it's entirely possible that the employer will come back with an alternative offer that takes into account more of your needs.
Keep in mind, this may not work if you haven't heeded the other recommendations in the series. It's important to show good faith in the negotiation process; you certainly do not want to walk in making ultimatums. But if you've gone back and forth a few times, and the employer simply cannot meet you where you need them to be, it's appropriate - and important - to politely walk away.
Do you have experience with this strategy? How did it turn out?