I think you could do it. Personally, I would want more than one outfit. Maybe three. Like a PP said, everything would have to be very basic and neutral.
Of course everyone's lifestyle and clothing needs are very different. And regional too. Around here, most people would not notice you wearing the same clothes over and over, as long as you were not wearing literally the exact same outfit every single day. You could get away with the same pants and different top two days in a row, or the same top with pants on this day and skirt the next. I recently visited a place where I can tell that people would notice and actually care.
I personally would feel satisfied with a minimum of outfits - I don't have any need to have new outfits to feel good. As long as my wardrobe was ok quality to begin with (and really, by ok quality I mean like, Old Navy - just not the Walmart crap that I seem to be stuck in myself).
I would also need some seasonal changes - not due to any fashion sense, but just practicality (weather). Though I live in a 4 season area, I might be able to get away with just 2 seasons of clothes though. I wear lots of layers, so winter layers can get stripped off in spring until I feel warm enough to reach for the summer clothes. And summer clothes can be layered with a winter layer in fall.
I would want some buffer for laundry in case I got behind, but if you consistently do laundry day after day, then you apparently have that settled.
I also second the travel thing. I just traveled and had access to washing facilities but I was sometimes too busy to wash (and was not really in control of my own schedule), and of course my parents also needed to wash things too. I wore the same 2 outfits every day for 11 days, not because I'm minimalist or that I even underpacked, but I just packed wrong (overestimated how warm I'd feel). Ah, but I did at least rotate the outfits so it wasn't literally the same two outfits, but I'd switch the pants and tops around.