A lot people ask for push support, so I think I will answer it here for everyone to see.
One problem with push is that Google Tasks do not have due time, only due date. Therefore I can't pop a reminder for you at the right time, the best I can do is pop it at 7am each day when there is a task to be done. It will only work when there is network connection, and I think you can just as well setup an alarm instead. This could be useful for people who don't have tasks for each day, but it's quite a bit low on the priority list.
The second problem with push is that if you make changes to your tasks using Google's web site my push server will not know about it and won't be able to notify you. I would need to write a big serve-side component that sits there and looks into your account all the time looking for changes. That's a lot of work for little benefit. The excessive load on Google's servers may also cause Google's ire, something to keep in mind.
Someone also mentioned that they would like push to sync data in background a-la email and calendar sync - that's not technically possible, sorry. Push doesn't transfer data.
So the bottom line is that there isn't much push usage planned any time soon.
