OK, I'll give this one a shot:
First, if you're "afraid" of losing the entire offer, then you aren't negotiating, you're begging. There is no negotiating if either side is not willing to walk away entirely. Negotiations are two parties coming together to explore the possibilities of an exchange and to go through a back-and-forth on terms.
If you've already committed to working there, even though you've never said it, then you're no longer negotiating. You don't have an "exit" option, and you are willing to take whatever they offer you.
Humor is a very bad idea at this point. If you don't take yourself seriously, then how can they expect you to take their business seriously?
This is your one and only opportunity to decide what your work is worth. That shouldn't be a number, it should be a range. You will listen to their offer, including the non-monetary compensation components, and decide if it is within your range or not. If it is, then you accept. If it is not, you say, "This is less than I believe my contributions are worth. Is there room for an increase in the base salary, or can you add ($x more per year / gym membership / public transit pass / free parking / additional vacation time / flying pony) to your offer?"
If they cannot, then you politely thank them for their time and consideration, and move on to the next offer or go back to your existing job.
It doesn't need to be at all confrontational. You are each stating the facts of your positions. You are stating what you are worth. They are stating what they can or are willing to offer. If they coincide, you have a deal. If they don't, then there is no deal. There is no confrontation. Neither side should be taking it personally or emotionally.
If this is not your mindset, then you are not negotiating.