first thing I'd check is the switch. Chevy CC switches are notorious for going bad...usually the wire gets brittle and breaks over time. I'd check this before anything else.
Here's what I did
Go to autozone or O'Reilly's. they should have the replacement CC switch/ turn signal arm in their "HELP" section..(or whatever they call it....the parts on red cards, for the little doo-dads that need replacing...like dome light covers and shifter boots)
Be very careful when opening the the box. Use a knife. Don't tear the box...you may be taking the switch back.
Don't worry about taking the column apart yet.
Look under your steering column....you should see a small wiring harness coming out of the column going under the dash. Unhook the harness, plug the
new switch's harness in.The wire should be long enough for you to lay it in you lap when you drive down the road.
Then, just make the switch as you would do normally. If it works, you've found your problem....go back home and install the switch in the column.
If it doesn't, wrap the switch back up the way it was new, and take it back to the store and get your money back.