Medicaid said that she doesn't qualify for this program because she is only visiting at this point and she is not a resident . That said, will the ER bill be considered means-tested public benefits? and will it become my responsibility if I sign the I-864 form?
If the ER pays the bill then it won't be considered public benefits unless you sign something saying that you are applying for public assistance. I would research low-cost insurance for her since she will be a US resident. You are agreeing to support her, so you should pay the bill, but technically they can't sue you to collect the debt, but they can go after her. I'd just see what happens when the bill comes and see if you can get a payment plan or a reduction.