To expand a little, I find that I can select all the 'orange' and 'red' tasks, and automatically set the focus to their badge-bearing containing projects (or inbox), using the following saved searches in Where in OF:

[Badged]->

tasks where (completed is false) and (due date < soon) and (((status of its containing project is active) and (effectively hidden of folder of its containing project is false or folder of its containing project is missing value)) or (in inbox is true))

[Orange]->

tasks where (completed is false) and (due date > now) and (due date < soon) and (((status of its containing project is active) and (effectively hidden of folder of its containing project is false or folder of its containing project is missing value)) or (in inbox is true))

[Red]->

tasks where (completed is false) and (due date < now) and (((status of its containing project is active) and (effectively hidden of folder of its containing project is false or folder of its containing project is missing value)) or (in inbox is true))

'soon' is defined by the setting under:

OmniFocus > Preferences > Data > Dates & Times > Due Soon

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