Negotiating an offer, is it too late? - 20 weeks in

I received an offer as a security officer and I think the pay is a little low. There are 3 people counting on me, so I am trying to be careful. I have a competing interview next week. What wording worked?

Thanks for writing this out. I went through something close to it 12 months ago, and it settled down once I kept a simple log of every call and form.