We did this 2 weekends ago and each made it with one carry on and no personal items!
I packed one outfit for every day, wore jeans on the plane, and brought one extra pair of shorts and undies just in case. I packed my clothes by day in space bags so if the TSA decided to go through my bag it wouldn't get all jumbled up or they wouldn't be touching my underwear! (Gag) It also frees up space. If you don't have space bags, you can use those big 1 gallon ziplocs and just squeeze all the air out.
Another thing, don't forget to check regarding liquids on the TSA's website. all liquids must be in containers 3 oz or less and fit within one single one quart bag. When you go through security, pull it out and put it in the tray with your shoes as well as anything that's not paper in your pocket. Keep your ID and your ticket in your hand as you go through the scanner, that's okay.
I even pack my purse in my carryon bag to go through security just so it's one less thing to grab later. Plus, knowing I have that much room in my carry on means I ca put more souveniers in it on the way home!
The other thing we do, and maybe our family is a bit weird, but we take clothing that is about worn out. Socks, undies, etc...and chuck them so we don't have to bring them back home. Are we the only people who do that? Not with all our clothes, just stuff we have that's about worn out. That also gives you more room on the way home for stuff.
I hope I didn't ramble too much. My husband and I fly a LOT so we've picked up on a few tricks to help us get through security and onto planes with less hassle. Best of luck and enjoy your trip!