Medicaid is a program with a long history of helping people with disabilities not only get medical care but live in their own homes rather than nursing homes. The program not only pays for things like operations, medications, and wheelchairs but for things like in-home care. Unfortunately, a lot of Republicans have their claws out for it. Many of them suggest replacing the program with "real charity." Let's go into why that won't work.
History shows that Medicaid is superior
Conservative/libertarian mythmakers would have you believe that before the New Deal and Medicaid, America was a place where charities, be they big national ones or simple churches, were always ready to step in without fail. History shows that this wasn't the case. Poor families who had a child with a disability often could not take care of them. They were often locked in basements, attics or sent to institutions (that were abusive more often than not). Private charity was not capable of addressing this. Medicaid changed things and provided a way for families to keep their children in the home.
The fact is, charity cannot replicate this. Churches, regardless of how many there are, do not have qualified nursing staff willing to work for free long-term. Not everyone can handle it. We are not talking about one-off operations. A lot of disabled people need lifelong care. Charities are not up to the task.
Furthermore, there is the money factor. Most charitable donations go to religious organizations. More specifically, the upkeep of your local church. According to the most recent statistics published by Charity Navigator only about 8% of charitable giving goes towards healthcare. A non-trivial portion of that is in the research for cures department. There aren't very many charities geared towards providing day-to-day care like Medicaid pays for.
There are some that provide one-off things like operations, home modifications and wheelchairs: Nursing care and job training, not so much. To put it bluntly, there aren't enough charity dollars to go around.
Medicaid provides charity to those that aren't photogenic
Charity and churches have another big disadvantage when compared to Medicaid. Only the charities with the photogenic people and celebrity backing get success on a scale large enough to be successful. Let's use St. Jude's Hospital as an example. The kids being served have cancer. They are all photogenic and smiling.They have everyone from movie stars to rappers as spokespeople. Their model of treating kids with cancer for free works for them only because these things are true.Not every disease or disability is conducive to TV commercials that tug at the heartstrings.
Not every charity gets the kind of celebrity backing that allows them to make commercials to start with.
If you need proof that being photogenic is what determines whether or not you get private charity, go to GoFundMe or any crowdfunding site. Full disclosure - when my wheelchair van was stolen, I was able to get a replacement through crowdfunding. However, I had local news media in two states backing me. My story was inspirational. For 99% of people considering crowdfunding, this simply isn't true. Many of these sites are filled with failed fundraisers. The determining factor at the end of the day is whether or not your story and photos make you interesting enough for a human interest story.
I'll admit that Medicaid has flaws. However, its biggest success is that it provides healthcare to poor people no matter how inspirational or mundane their story is. Whether they are a poor kid in the wheelchair with a 4.0 GPA with Ivy League aspirations to the random guy that's just scraping by, they can still get basic healthcare.