Have no fear, that is not rust in your kettle! It's very likely buildup from intensive use, especially if you're using tap water (but it happens even with filtered water). Filling the kettle with a vinegar and water solution, and letting it soak overnight should allow you to clean it thoroughly the next day. 

You may also try our descaling tablets. Simply add about 8 oz of water to your unit, drop in a tablet and let it dissolve. Allow the solution to sit overnight, then pour out in the morning. Clean well and your kettle should be ready to brew!