Medicaid is a state run program, so it might very per state, maybe more "liberal" states qualify more people for Medicaid.
Honestally I think all we have to do is make everyone qualify for Medicaid. If you qualify for Medicaid it is a great program, better then most private insurances. It covers dental too.
The way the system is set up now, I think we are actually encourging people who qualify for Medicaid to stay poor, because the instant you fall out of your "bracket", you lose coverage. Some people rather stay poor and have healthcare then to be slightly over Medicaid's definition of poor and have no healthcare.
And in the conservative sense, that's more "fair". If you pay taxes, you are paying for Medicaid, but if you pay taxes, you are probably not getting Medicaid. If you give Medicaid to everyone, even taxpayers benefit from it.