This is an electronic version of a "bring forward" filing system that has been around for many decades. An older friend of mine showed me his "bring forward" file: it has a file for each month and also a file for each of the coming four weeks (labeled 1, 2, 3, 4, and 5 because some months have five weeks).

He just puts things - like bills, for instance - in the appropriate folder depending on when they're due. And then once a week or month has passed, it gets rotated to the back of the box. It's a great approach; a digital version would replicate the same concept and would be particularly useful if it incorporated the notion of attached documents such as invoices.