So I had this problem with a 2006 Malibu Maxx I purchased in February and today I solved it.
First, I tried removing the CDs with tweezers but they were too tall and couldn't open when inserted a 1/2" in the player. Then I thought my next option would be to take apart the dash and CD player its self. BUT before I started, a light bulb went off in my head.
I went back into my house and grabbed two butter knives.
1. I inserted one under the lowest of the two CDs and placed one on top of the highest CD.
2. I then hit the eject button so the two small metal "CD holders" would drop down.
3. Once they dropped, I pressed the two butter knives together and gently pulled the CDs out.
That's my 30 second fix and I hope this helps someone else.