Find the line which says KeepAlive and turn it off.

Out of the box, the configs which ship with Apache on e.g. Ubuntu are virtually engineered to fail if your blog ever gets a traffic spike.

Options:

Install a caching plugin for Wordpress.

Copy the output of Wordpress for that blog post to a static .html file and use mod_rewrite to point requests for the post to that file.

Turn off plugins you don't need.

Install a reverse proxy cache (such as Varnish) in front of Wordpress.

I'll add a really low-tech solution: add the text in a toplevel comment.

Either

a) Throw more resources at it. I am not sure how it is done, but cloud can scale on demand from what I know.

b) If not using already, use some static page serving plugin for Wordpress, like WP Super Cache or other. This should reduce some load.

I have chaching enable. It's apache that is dying. Does anyone know how to transform a t1.micro instance in something bigger or how to throw more resources?

What is your worker configuration for Apache? You can make it much hardier with some tweaking, or you can get even more robust by switching to nginx, or you can hit lightspeed by putting Varnish in front of it (listed in ascending order of complexity)

You could host your blog on Amazon S3. Unless there's a really compelling reason why you need to dynamically generate your blog on every request, serve it up as a static website. That way you can use your micro instance to do the generation and push it up to S3 which frees it up to do whatever other tasks you want while S3 does the serving.

Ditch Apache for Nginx, Lighttpd, Cherokee, etc.