Bring a small bottle of woolite and/or detergent in your 3-1-1 bag. If you hand wash underwear, socks and tops in the sink you can bring much less clothing along.
I find nylon underwear dries overnight, but cotton socks and tops take 12 hours. If you wash [i]yesterday's[/i] outfit when you arrive at the hotel, say by 7, (takes about 10 mintues) then hang it to dry, it should be good by 7am to pack or wear again.
Both Rick Steves and Amazon.com sell a braided rubber clotheline. Check out
www.onebag.com/ for really good packing advice. Also the Rick Steves Graffiti board under "Packing Light". .