There appears to be a glitch with Gmail and iOS 6
I am having the same issue with my Gmail accounts on the devices that I have updated so far. No issues with the devices still on iOS 5.
Pop up states that settings need to be checked. However, the Gmail finally comes through after a delay of at least 5-15 minutes in iOS 6. It appears the Gmail servers are not playing nice with iOS 6. Hopefully, they rectify the situation soon.
Also, phones on iOS 6 are initially having difficulty keeping the wifi connections. Reboot of the devices seems to correct the issue.