Negotiating pay when I have been out of work

I have been out of work for 3 weeks and feel pressure to accept less. I do not want to price myself out. Does giving a range hurt?

I gave a range based on local postings and said I was flexible depending on the whole package. They did not push back.

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