Negotiating an offer, is it too late? - any advice?

I received an offer as a marketing coordinator and I think the pay is a little low. There are 5 people counting on me, so I am trying to be careful. The hiring manager was friendly and open. What wording worked?

Thanks for writing this out. I went through something close to it 10 months ago, and it got easier once I kept a simple log of every call and form.