The whole Tor network advertises 6 GiB/s according to the metrics page. DE-CIX statistics say they have an average bandwidth of 200 GiB/s. So if you assume that web traffic is roughly 20% of all traffic, we talk about 40 GiB/s. Numbers between 5 and 30% are 2 to 12 GiB/s of traffic in the DE-CIX case.
So if those estimation is correct, Tor should be able to handle (DE-CIX) web traffic right now. It would need some fast relays, but not enormous amounts of relays. I assume the numbers don't grow that much on a worldwide base. So with a fair number of fast relays web traffic should work.
However when when talk about general Internet traffic (BitTorrent alone is estimated to account for >40% of internet traffic), you will needs ten of thousands, if not millions of relays. A client will have to download all those information at the beginning. I would estimate that this file can easily grow to some hundreds of MB. Furthermore, as Peter wrote, every relay talks to each other which simply doesn't work with so many relays.