The “quota exceeded” error is related to YouTube dramatically reducing API quotas for all of their users in recent months. To get up and running, repeat the YouTube API key setup procedure and save the new key at WP Admin > Settings > TubePress > Feed > Google API key.
We’d also suggest adjusting your cache settings to make them more aggressive. Here’s how:
Enable both the API and HTML cache at WP Admin > Settings > TubePress > Cache
Set the lifetimes of the caches to the highest value you can tolerate
43200 seconds (12 hours) would be a good starting point. Higher cache lifetimes will reduce quota usage, but the drawback is that you might see stale data served up from the cache (e.g. if you update your videos multiple times a day).
Please let us know how that goes and if we can do anything else to assist!