It's also wise to rotate the tires. If the problem goes away then it could be something as simple as a poor tire balancing or in an extreme case, the tire compound isn't correct throughout the structure causing its own imbalance.
I always try to look at the easier things first. If the G6 was rwd, I'd vote for an out of round driveshaft. Worst case is a CV might be kaput. If you rotate the tires, and get an alignment done (not at a cheap place!) the tech will tell you that the alignment couldn't be properly set due to (insert part here) failing.
When my G6 had about 10K miles on it the steering went from perfect, to sloppy with about 1" of excessive play. After a few days in the shop the tech's couldn't diagnose the problem to one particular part, so everything was replaced, rack, intermediate steering shaft, and the electric motor assembly. Not a problem since.
'11 Ram SXT 4x4 quad cab - 5.7L V8; 128,200kms
'09 Malibu 2Lt 3.6L - 140,000kms purchased 1 March 2019
'06 Pontiac G6 GT - 3.5L V6; 162,000kms (rear ended 15 Feb 2019, and given totalled title by insurance)