That should work. I had a bag similar in size (16x13x8) that worked with considerable shoving, squeezing, etc... (the 13 dimension was the problem), no guarantees, though. However, if it is soft-sided, you could always take 1 or 2 things out and it'll fit (keep a plastic grocery bag either in your pocket or an easily accessible place, and use it if you need when you get on board).
US is usually good at getting bags out quickly, and I've never heard of them loosing a gate checked bag (at least on CRJ's and EMB's).
How long is your flight?