If the donations go directly to your cousin, they would count as income in the month received and anything not spent within the month will count as an asset in the following month, possibly disqualifying her from Medicaid until she has spent the new money back down to the $2,000 cash limit. A better idea would be for the contributions to come to an entity other than your cousin herself. That could take the form of a trust or bank account. (Because the donations are for the use of a single person, there would be no charitable deduction permitted.)
Another possibility would be for the funds to go directly to the hospital or some kind of fund they can establish; you may want to contact them to see how they have handled this type of thing before.
