There are subscriptions for various levels of support, from $50/mo for 12 hour response time to $15k/mo for 15 minute response time.
The relationship between the pricing tiers changes fairly drastically, depending on how much you are already spending on Amazon Web Services. Gold, for instance, starts out at 4x the price of Silver support, but by the time you're spending 80K/month on services, it's only a $900 premium (and stays there no matter how much bigger your bill is). At the $150K/month level, it's a 2x jump from Gold to Platinum, which may or may not be a huge jump, considering the extra level of service you get.