Gina,
The Mountaineer's Route can certainly be accomplished in one day, especially in good conditions and if you're already familiar with the route. I have photo documentation of the whole route, which I could e-mail to you if you'd like (rob.spinosa@flagstar.com).
In any case, in May of 2000 I arrived at the Portal on a Saturday morning, hiked up to Lower Boy Scout Lake and stashed some food and water there. I hiked back down and slept at the Portal that night. On Sunday, I got an early start, and was up and down in under 9 hours. I had done the MR several times before that, and knew what I was getting into. I traveled very light. The crux is definitely the short section after the notch and right before the summit. Mark your exit onto the summit plateau with a wand or other gear.
Good luck and be safe. On a nice day, there is nothing like being up there with the Lower 48 at your feet....
Rob