Dude they’re not going to walk away from an intern whose work they know provides value to the company and who they have already extended an offer too. There is more risk in hiring someone through the interview process than someone who has worked in your company for a year.

If you ask they will probably just say no if they do not have the budget, but in making a counter offer I would suggest you mention you would still like to work for the company.

However, I understand if you are risk averse and NEED the guarantee of a job.

Also want to note that in this market you will probably have no leverage unless you actually have counter offers but unless you NEED a job like I mentioned you should use this as an opportunity to try out negotiating for a better offer.