I wonder if there is a way to ask photoshop to save for web and devices using the default options, and save two or tree mouse clicks each time.
You could memorize the shortcut (Ctrl/Cmd + Shift + S) > hit Enter to save.
If you feel the shortcut is too long you can always define new Keyboard Shortcuts.
But if you truly want a one-click solution you can record an action and assign a function key. You can toggle the dialog on/off from the actions menu so it doesn't prompt you for the file name.
As Thgaskell mentions, the shortcut will save you time and clicks.
But since you highlight you need the default settings each time, it makes me think of two things: You either want to use the same custom settings for all images, or you want to erase them every time you save. In both cases, the best way to go is probably to save a preset for the Save for web.
You can do this by making your choice of format, quality, etc as always, and then click on the little icon to the right of the Preset dropdown list > Save Settings.