This is basically a misunderstanding of how budgeting works. Or, at the least, it's predicated on the listener misunderstanding how budgeting works.
What they're doing is switching between two questions very quickly. The first question is: "How much money are you cutting from Medicare?" The second question is: "How much overall deficit reduction is contained in your plan?" And the second question isn't getting answered.
Here's what everyone agrees on: Ryan and Obama include the same cuts to the Medicare program itself. So if you're an insurance company participating in the Medicare Advantage program, you're getting the same cut no matter who wins the election. So the answer to the first question is, "the same amount as the Obama administration."
What Romney/Ryan are saying is that they then take the money saved from their cuts to Medicare and put it toward deficit reduction while Obama takes that money and spends it on health care for poor people. The argument here is that by using the money to cut the deficit, Romney/Ryan make future cuts to Medicare less likely.
But Romney/Ryan also add a trillion dollars to the defense budget. And they have trillions of dollars in tax cuts they haven't explained how they're going to pay for. So those decisions make future cuts to Medicare more likely. Meanwhile, Obama cuts defense spending by hundreds of billions of dollars, raises about $1.5 trillion in new taxes, and puts all that money into deficit reduction. So that makes future Medicare cuts less likely.
So if the argument is that Romney/Ryan protect Medicare by putting the $770 billion in cuts towards deficit reduction, Obama protects Medicare by twice as much by putting the $1.5 trillion in new tax revenues towards deficit reduction. So far as the deficit is concerned, there's no difference between a dollar from Medicare and a dollar from taxes.
Which just leaves us where we began: Romney/Ryan want to do more of their deficit reduction by cutting social services while Obama wants to do more of his deficit reduction through raising taxes. Deciding whose plan makes more sense requires making judgments about whether Romney/Ryan will ultimately pay for their tax cuts. But deciding who is cutting Medicare by $700 billion just requires looking at who is cutting Medicare by $700 billion. And at the moment, that's both Obama and the Republican budget.
The Romney/Ryan campaign is aware of the difficulties in their argument, and so they've introduced a new wrinkle. They told Avik Roy, who also serves as a health adviser to the campaign, that "A Romney-Ryan Administration will restore the funding to Medicare." If that's true, then their budget math just got completely impossible, as I'll explain in a coming post.