It will probably fit, and I echo Coastie's advice and add some more:
1) Try wheels in first and if that fits, go that route because it makes it that much easier/faster to unload when you deplane. If wheels in first does not fit, then try handle in first. If you constantly are finding that on most planes your bag fits wheels out, but not wheels first, then obviously put it in wheels out.
2) Some planes, like MD-80s have narrower bins on one side. For those, you probably have to turn the case sideways, but always try to place your bag wheels first in the deeper bin side IF there is space available by your seat. Now, that leads to the next one...
3) Never be that inconsiderate bastard that walks onto a plan and puts his or her stuff in the first free overhead bin available and then continues on to the back of the plane to your ticketed seat. Think about it. If everyone did that, then no one would be able to get off as all the people in the people in the front would have to fight to get to the back to get their luggage. I know it sounds crazy, but I see some inconsiderate knob or two do this on EVERY flight.
4) Make sure to limit your carry-ons to one personal item and one rollerboard case, and tuck the personal item under the seat in front of you. If everyone did this there would be no "running out" of space and the need to check bags.
5) When deplaning, don't bully past people that are trying to take their bags out of the overhead bin. If you are late for a connecting flight, ask the flight attendent to make an announcement asking people deplaning that are not pressed for time to stay in their seat. Then, if you can, and people are seated, deplane as quickly as possible. But, don't push and shove to get out of the plane. You shouldn't assume the value of your time, or your right to get off the plane quickly is any greater than anyone else in front of you.
I travel by air a lot, and I exclusively carry-on, and I follow these rules and really appreciate others that do the same. By not having to check bags it saves me a sum total of what is several days, if not close to a full week of my time each year; not to mention the cost savings for my company of not checking bags. Lastly, I try to stay calm, even when crap happens, and it does when flying. There are things within my control that I can fret over and work to change. Air travel is NOT one of those things...
TJR