No tent, meaning staying in motels?
I try to do sink laundry every night if I think the air is dry enough that my laundry will be only slightly damp by morning. Thus, I usually just bring a couple days worth of stuff. And if I get a few more days of wet weather and can't do laundry for a few days, I keep wearing it anyway.
If you are in motels, some motels have coin op laundry machines. On a couple trips where I expected to have laundry machines, I brought some of those laundry soap packets from home.