How big is too big? By the time the blockchain is 1 terabyte, we would all be using 16 TB solid state drives or larger, like the one Samsung showed off this year.
People heavily invested into bitcoin will be running a separate server just to host their own full node.
The Bitcoin network can currently handle 7 transactions per second. At 250 bytes per transaction on average, the blockchain is growing at 1.75KB/s- easy peasy. But if we want a network that can handle a million transactions per second, the blockchain will grow at 250MB/s, 15GB/m, 900GB/h, 21.6TB/d. That's way too much data for most PCs and way beyond the typical bandwidth of most cable ISPs.
We aren't going to handle a million transactions per second. Not even visa, one of the biggest payment processors, handles that much. They only handle around 3000 transactions per second, so we should target that.