What to do if a university is pushing for a response before making a formal offer for a tenure-track position? I have interviewed for a tenure-track position. I got a call (followed by an email) saying that they would like to offer me this position and I am their top candidate.

This being said, in the negotiations that followed for a few days after, the department showed no desire in increasing the salary or startup package (which are already pretty low compared to other institutions). This is even after I told them that I have two other offers pending.

I have not seen the formal letter yet, and they are pushing me for a response only a few days after they offered the position on the phone.

I feel like they are low-balling me and being very aggressive. What actions should I take?

BTW, I asked for an extension and they gave me less than a week.
"I would like to see a formal written offer before we move forward."

Any department that's unwilling to do that is sending up huge, brightly colored red flags. With fancy gold tassels. And embroidery that reads "DANGER".