I have several lists of Google tasks, I have an app for my iPad that lists all Google tasks regardless of what list it is from by due date. So it does appear the API supports doing this.
I'm looking for a similar feature when using the browser/Windows. On my PC I tend to use this URL (https://mail.google.com/tasks/canvas?pli=1) to get a 'full screen' version of tasks, but I still must look through each list to find out what is due today/tomorrow.