I was able to do it for 12 days of Hawaii travel from east coast. I was a horrible overpacker. Decided not to check a bag because the fees just irritate me (although I upgraded with miles and wouldn't have had to pay).
I still had 3 shirts that I never wore. As long as you have W/D it can be done.
Took old sneakers for hiking that I threw away before we left. I only took 1 pair of comfy sandals in tan to wear with anything for dinner out, and a pair of Tevas that match my swimsuit and board shorts for the huge amount of time we were swimmimg, snorkelling, boogieboarding, etc.
The best way to do it, if there is something you want to pack that you will only wear once, leave it at home....and pack only your favorite shorts/shirts that you know you will wash and wear again.
I had some room left over in the backpack I carryed on, that left me room for souveniers, most of which were shirts. Good thing hubby had some room too, because Hawaiian interisland coming home made me weigh my large carryon and would have made me check it and pay if I didn't get it down to 25 pounds. I was 10 pounds over because I had all of our dirty laundry in a garbage bag for the trip home.
This was with hubby taking a PS3 and our laptop as well...oh and taking home the snorkel, mask and diver fins I bought at ABC store (good silicone set that didn't leak, paid more knowing I would keep them).
Good luck, you can do it!
PS if there's a guy travelling with you, they usually don't have a full quart size ziploc bag full of toiletries, so mix your stuff together to maximize space. TSA just cares that 2 people have 2 clears bags. And my guy doesn't mind using comp. stuff from hotel, that's less you have to take.