Medicare is for the over 65 population, people on disability can access it before age 65.
Medicaid is, in each state, a state program that is partially paid for by the Federal Government. (Therefore, by all federal taxpayers.) You've been hearing about the various states complaining that the Federal government should just "block grant" the funds, rather than the current program that sets minimum standards that the states must follow for the use of the federal dollars. They want to use the dollars anyway they see fit.
https://www.cms.gov/MedicaidGenInfo/
Some states, like NH, are what is called "Donor States" we get back $.71 for every tax dollar we send to Washington. New Mexico gets $2.30 for every dollar they send. Medicaid payments to the various states makes up a very large part of these dollars. In effect, we are sending tax dollars to any state that is getting back more than they send in.
These data are from 2005, I've seen the 2009 data, but can't find the link.
http://www.taxfoundation.org/research/show/266.html
IMHO, NH needs to lobby very hard for a more fair share of those dollars.
But, by far, the largest contributor to more pressure on Medicaid is the unemployment problems in the country. Unemployed people are far less likely to have health insurance. No Insurance, get sick, Medicaid ends up paying, and taxpayers end up with the bill.
While I understand the gut level objection to a national health plan that is paid from general tax revenue, county's that have such programs spend far less on healthcare than we do per capita. (Many with better health outcomes...)
http://www.kff.org/insurance/snapshot/OECD042111.cfm