When bitcoin is actually "mainstream" and the volumes of transactions that we are seeing today, is becoming a normal thing, how will the network handle it?
Through a increased fees. Imho the fee market is underdeveloped. We need a better and more aggressive fee system. That's the prime way to prevent spam attacks: Just make them economically unfeasible.
For those worrying about their dust transactions: Those will go off-chain or side-chain, so Bitcoin can scale without wasting resources and maintain its decentralized nature.
ya.ya.yo!