A NYT piece discussing the prospects of another budget deal would have benefited enormously by answering this question. The piece referred to a proposal to restructure Medicare under which the government, "could potentially charge the affluent elderly more."
The definition of "affluent" matters enormously. When it came to raising taxes, President Obama and the Republican leadership agreed not to raise taxes for couples earning less than $450,000 a year. If this same definition of "affluent" is applied to elderly then it would only affect 0.1-0.2 percent of Medicare beneficiaries.
While the rich have a hugely disproportionate share of the country's income, their per person Medicare expenses are roughly the same as everyone else's. (Actually they would be somewhat less since the premiums for the program are already means tested.) This means that if President Obama and congressional leaders are planning to apply a cutoff for being affluent for Medicare that is comparable to what was used in the tax negotiations then the amount of money at stake is trivial and it is hardly worth the paper's time to be reporting on the negotiations.
Alternatively, if the proposal is intended to raise a serious amount of revenue then it will likely mean that seniors with incomes around $50,000-$60,000 would be paying more for their Medicare. This is not a level of income that is generally regarded as "affluent." If this is the sort of cutoff being considered in the negotiations then the NYT is badly misleading its readers by saying that they are discussing charging fees to the affluent elderly. In this case they are talking about charging higher fees to people who almost everyone would consider middle income.