Views with content that ...'expire' after a certain time ???

I'm trying to create a view that only lists content from the current day through the past two weeks.

For example: Special Announcements to site admins.
I want to create the announcements every so often, and then have them appear in the view block within a two week window of the current date, and then once the announcements creation date is older than two weeks, it will no longer be listed.

The Views filter 'Node: Created Time' looks like I can only set it greater/less than an absolute time/day. So that makes it possible to show announcements that were created within two weeks of today. But, what I want is to make the Created Time window relative to the current day (whether that current day is tomorrow, next week, next year)...

Other alternatives I'm considering:
Do it with Arguments and Argument handling code... Maybe use argument: Node:Posted Week, and create some Argument handling code that figures out the current and past week and passes it as an array.

Or forget Views and create a block php snippet that just displays (x) nodes with a creation date within (x) days of (current) date...

I was just hoping this had already been figured out by Views (or figured out by someone else)...

If anyone has any advice, I'd like to hear it.