Congrats on your book!
Look into 1-hr dry cleaners in towns before your trip. Might be nearer your book signing than hotel. Check ratings & maybe even contact them in advance (esp if you have a particular city you are worried about - short stay and big TV interview the next day, etc)
If necessary, you can mail yourself clean clothes to a hotel midway through the tour if you really don't think you'll make it through the whole tour.
Compression (or zip-lock bags) with the air squeezed out can really shrink the space needed for socks/underwear.
And remember you are allowed 1 carry on + 1 personal item (briefcase / small backpack) in case clothes, toiletries & electronics are a bit much for your single bag. And wear / carry your jacket - don't worry about fitting it into your bag.