I'd like to tell you it's OK to tip it and do the repair, but there's a good reason it's better to remove the cabinet. For one thing, you have to remove the pump, then the motor in order to replace the coupling. Trust me, it is easier to do when yu have room to slip the pump off and tuck it to one side, then remove the screws and motor brackets. Myself and a few select seasoned technicians can do this lying down with the cabinet intact, but only because we have been thru the motions hundreds of times. I don't suggest it for you, rookie.
The other problem is when you lay one of these over, you almost double your chances of breaking a tub spring or bending the mounting plate. 90% of those who do this complain of balance problems later. (You'll thank me)
The cabinet takes a couple of minutes to remove. Save yourself a callback and make momma happy by doing it right the first time