I want to search my menu bar, to easily find obscure menu items.
I know that the HUD (Heads Up Display) in Unity has this feature, however I am running Gnome 3 on Debian 7.
Is there a way to do this on my system?
Sadly, no. The gnome shell doesn't include such characteristics as Unity. There were some projects like Synapse to make this possible in any desktop environment but it's dead. There's also Conky and Gnome-do but it functionality can be lacking.
I recommend you try
It is based on
Rofi and works like a charm for me on Ubuntu MATE.
There is a project called "plotinus" that does just that: https://github.com/p-e-w/plotinus and it is designed to work with every GTK3+ application. I feel like it is still WIP. I managed to make it work with gedit and nautilus but not easily.