proper use of the Cache-Control header will make life better. With that header you can tell a browser how long the content is good for. If it is something that never changes, you can instruct a browser to keep it for a year. If it frequently changes, you can instruct a browser to keep it for an hour, or a minute, or revalidate every time. You can give similar instructions to a CDN.
Here's a good guide, and here are some examples:
# keep for one year
# keep for a day on a CDN, but a minute on client browsers
Cache-Control: s-maxage=86400, maxage=60
You can add this to pages served from your EC2 instance (no matter if it's nginx, Tornado, Tomcat, IIS), you can add it to the headers on S3 files, and CloudFront will use these values.