There are a couple things you can try. First, try uninstalling your google account, restarting the tablet and then readding the account. This may resolve it for you.
Should that not work, then we are sadly at the more serious fix, which is to "Hard Reset" the device. Since this will wipe all data on the device, and make it start over fresh, you may want to try and back up what you can (files, videos, music, contacts, etc. to a computer or other device). You can't back up apps, so that would all be lost.
NOTE: Doing this will clear 'all' the data on your tablet, so it is suggested you not choose this option unless you have to, or aren't worried about losing anything on the device.
Be sure you back up any data you want to keep, to a...