Another possibility, if you can store the data in a simple format in a file, you update a file with the data and use the web server to check its timestamp.
Then the browser can poll, making HEAD requests, which will check the update times on the file to see if it needs an updated copy.
This avoids making a DB call for anything that doesn't change the data, but at the expense of keeping file system copies of important resources. It might be a good trade-off, though, if you can do this for active data, and roll them off after some time. You will need to ensure that you manage to change this on any call that updates the data.
It shares the synchronization risks of any systems with multiple copies of the same data, but it might be worth investigating if the enhanced responsiveness is worth the risks.