What do I do without POA for my mom when I need to set up a QIT to enroll her in Medicaid?

Medical POA will not work here it is a financial thing. You are going to need a lawyer to set up a trust make sure its an Elder Lawyer. He may be able to help you find a way getting around a POA.

Elaine, I read your profile and it looks as though your mom is already in care.
If this is so, speak with her care center now if her funds are running out.
They may be able to assist you in getting her Medicaid coverage.
OR they may put you in the right direction of someone who can have you assigned temporary guardianship to apply.

Should you wish not to take this on tell the facility that you are unable to take on guardianship and it's too late for POA papers. Inform them them that they will need, now her funds are almost gone, to apply to have state guardianship for her so that her SS and medicaid funds come to them for her care.

They cannot discharge her unsafely as she isn't competent for discharge, so they will handle this if you are unable to.

You can also consult with an attorney to look at best options.

I sure wish you the best of luck.

What did the attorney that is doing the QIT say?

Ask about emergency temporary guardianship, this may be the easiest way to be able to provide advocacy for your mom.

I am sure others will offer more info but I would think that the Medical POA would be sufficient if not you may have to obtain Guardianship.
Are you trying to do this on line or can you go in and talk to a real live person?
Would the AL facility be able to help with this?