I'm a college senior and I'm applying for my first full-time position. I recently got an offer for around $70k for a data analyst position. HR initially told me that the salary was negotiable, so I submitted a letter of justification (per their instructions) with my desired salary. According to a friend who works there, the head of the department thinks I'm the best candidate for the job and went to HR to get approval for the higher offer.
However, this made HR very upset for some unknown reason, and HR stonewalled them. I then received a phone call from HR telling me that they are no longer willing to negotiate salary, and I also only have till the end of the week to give them an answer. I explained to them that I'm in the interview process for other companies and will need more time than the end of the week, but they seem extremely resistant to giving me any more time and essentially told me that they'll call again on Friday, and if I still haven't made a decision, I can turn down the offer (although they implied there's a chance they might revisit an extension when the time comes).
Is there anything I can do at this point to get a better initial offer? My friend told me that he got a significantly higher offer after negotiating for the same position last year, so it seems that I've just gotten caught at the butt-end of interdepartmental drama. It definitely sounds like the department head really wants to hire me, so would it be wise to email them directly? Perhaps I could get them to push harder on HR to get approval for the salary if they know that I'm inclined to turn down their offer. I'm worried that dealing with HR further won't go anywhere since HR won't be negatively affected if the other department loses me.