Negotiating an offer, is it too late? - what worked for you?

I received an offer as a call-centre agent and I think the pay is a little low. I am in Baltimore, in case local advice matters. I have a competing interview next week. Did it backfire?

Most employers expect a short conversation. Mine did not even blink.

I thanked them and said I was excited but hoped we could talk about the pay. They came back with a bit more.