The key to a good cleaning is gaining access to the blade housing (as Bruce mentions). I am not familiar with Sears but I know higher quality mowers such as Simplicity and Airens, the deck can be easily dropped down and released for cleaning.
My dad is 70 years old and cleans his housing with a powerwasher. You don't need full pressure to do this. He needed a mower that could be easily maintained. So he spent over $3000 for better quality. I know you have a Sears and probably like it. But if you find yourself buying a new one in 10 years, well, you know. I do hope it works out for you. I usually end up only buying Sears hand tools (lifetime guarantee). From experience, both personally and from others, I stay away from everything else that has 'power'. Getting replacement parts or repairs was always a nitemare. Even for simple things like a grill!
Best to ya and hope what little I have to offer helps. :)