Large super-majorities of the public oppose cuts to SS and Medicare. This, by the way, includes self-identified conservatives and Republicans. In large part this is the public being ignorant and wanting something for nothing--if the public had their way, we'd balance the budget and double Medicare and SS benefits by cutting foreign aid payments.
That said, for something as important and widely supported as these two programs, we should be discussing solutions to their long-term funding issues as a standalone debate. Cutting them after a month of backroom negotiations while using the credit worthiness of the USA as a hostage strikes me as very inappropriate and not politically sustainable.
Edited to add: the reason these cuts are stupid is because many of them would come into effect immediately, which would be disastrous for our already weak economy. The size of the cuts are appropriate if projected into the future and not the immediate present.