After a few days of data connectivity hell for some Nexus 6 owners, it seems that Google performed a fix on the back end. Comments on a post in the r/Nexus6 subreddit indicate that most people have had their LTE data connection restored by this fix; however, many are reporting that they fixed the issue themselves by changing the APN settings or by updating their Google Connectivity Services through the Play Store.
As of now, it is unclear how exactly the issue was fixed, but a Google employee named Orrin (u/GoogleNexusCM) posted an update on both r/Nexus6 and the Nexus Help Forum on Google's Product Forums. Orrin explained that the data outage was caused by a problem with GPS, although he didn't go in depth.
It seems like most owners affected are on T-Mobile, but there are a few reports of issues from people on other carriers.
If you're a Nexus 6 owner and you're still having issues, perform a restart on your device. This fix was made on Google's end and does not require an OTA update.