Original Pixel and Pixel XL are hit with SMS bug that prevents messages from getting through
A manager from the Pixel User Community wrote that "the team" is aware of the problem and is indeed working on a fix. The post also suggested that some Pixel and Pixel XL owners with the SMS issue were able to exterminate the bug by rebooting their phone, or by performing a factory reset on it.
Unless you want to wait for Google to push out an update, trying a reboot is a rather innocuous option. If that doesn't work, the factory reset would be the next thing to try. While you might be loathe to press that button, if you do get desperate enough to eliminate the problem, make sure that you back up your data before starting the factory reset process.
source: PixelUserCommunity via AndroidCentral