If they're offering you a job, they're pretty interested. It's expensive to hire people, once they're making an offer, you have a good amount of leverage. I've gotten progressively more aggressive with negotiating over the years and, as long as you aren't a jerk, the worst that's going to happen is they'll say no to your counter offer. Try it out and just push yourself past your comfort level a little bit each time you have those conversations.
How would you suggest determining how much they need you, when you're really not sure?
If they're offering you a job, they're pretty interested. It's expensive to hire people, once they're making an offer, you have a good amount of leverage. I've gotten progressively more aggressive with negotiating over the years and, as long as you aren't a jerk, the worst that's going to happen is they'll say no to your counter offer. Try it out and just push yourself past your comfort level a little bit each time you have those conversations.
That's a really good point, Rachel!