The news that cutting Medicare is unpopular and taxing the rich is popular shouldn't shock anyone, but I think the partisan breakdown on Medicare really hasn't sunken in with the media conventional wisdom yet.
But the unpopularity of Medicare cuts among the Republican grassroots is a straightforward consequence of demography. The GOP has increasingly become the party of people for whom anti-gay messages or appeals to white anglo ethnocentricity resonate, and those are the groups that are most likely to love Medicare. Republican politicians have tried to accommodate this reality in a number of ways. In 2003, they made Medicare benefits substantially more generous. Then they spent 2010 complaining very loudly about some rather minor Obama administration cuts in Medicare reimbursement rates. Then they spent 2011 campaigning on a promise to drastically cut Medicare benefits, but not for anyone born in 1956 or earlier. Then in 2012 they pivoted back to complaining that Obama had cut Medicare. Now they're insisting that a budget deal needs to include large "structural reforms" to entitlement programs (presumably including Medicare) but they won't say what this means.
This kind of awkward position is by no means unprecedented in American politics. In the 1950s and '60s, Republicans favored less military spending as part of an overall pitch for less spending. But since the Reagan era we've taken for granted that "small government" is compatible with lavish expenditures on ships and planes and bombs, so there's no reason in principle that you can't be both the party of tax cuts and Medicare spending. But the turn hasn't yet really been made, so the switches in policy and rhetoric get confusing.