Short answer: You should update your browser.
The recent version of Chromium is >= 54, and Google Chrome is also at >= 54. Chromium 37 is several years old, and many things have changed through all these years.
From here, we see that there were no updates for Chromium 37 in Ubuntu, and many people stuck in version 37.
The OP is correct, there is no Chromium update to 37 for Precise. This
is a known bug and has been reported to launchpad bugs. The stable
repository has not been maintained for a few years and adding the
"stage" repository will result in upgrading to 48 which won't work on
12.04. As of now this is a problem as 37 is not compatible with the latest libnss3 update and any machine with chromium 37 & libnss3
update can't access google sites or content.
It seems that the same is true for Debian. Please upgrade your browser from the Chromium website, or download Google Chrome instead. It should fix the problem. But note that Google Chrome voilates many of Debian free software guidelines.