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I was admitted to Cardozo a few months ago and was able to renegotiate my scholarship from $16k to $26k/year. I put down my first deposit there about a month ago.

I just found out I was admitted to Fordham at sticker price - they told me over the phone when they gave me my offer that they would be unable to give me any money.

Is it worth it to go back to Cardozo and try to renegotiate again based on my Fordham admission? Could there be any negative consequences to telling them I am considering another school when I've already put down a first deposit?

No, there's nothing bad that can come of negotiating further. I informed Cardozo after I got into a better school off the WL and I got a much better (+$12k) offer soon afterward.