Say you get four weeks paid vacation at your current job and the new one's only offering two for new hires. Don't try to force them to give you four, just force them to toss you a bone to make up for the ten days per year of your life you're going to be giving up by coming to their company. I'm sure that's worth another 10-20% to both parties. Alternately, walk away if the four weeks really is a deal-breaker for you.
Are the people who "can't" negotiate and who blackballed you living under the same paltry vacation package you were offered? I'm assuming you didn't ask about vacation until after they made you an offer. To do otherwise is to chase off a possible opportunity before they've committed to you. Once you've got an offer, recognize that multiple parties at the hiring company are committed to seeing the deal go through, so you have more bargaining power than you did at the "we're still deciding who our top candidate is" phase.
Are the people who "can't" negotiate and who blackballed you living under the same paltry vacation package you were offered? I'm assuming you didn't ask about vacation until after they made you an offer. To do otherwise is to chase off a possible opportunity before they've committed to you. Once you've got an offer, recognize that multiple parties at the hiring company are committed to seeing the deal go through, so you have more bargaining power than you did at the "we're still deciding who our top candidate is" phase.