Great idea! While I do agree that it’s more motivating than setting up a bank account (or even a “piggy bank”), I do have some suggestions:

1. Let the user select how much he wants to put aside. Not daily, but maybe at the start of the week the user can pick the sum of money he/she wants to save up each day, since some weeks you can find yourself almost broke, while others you may have more money.
2. More entertaining than a push notification, at least for me, is a home screen widget. Maybe something simple, like a small cartoon picture that resembles the goal (e.g. suitcase for trip, cartoon image of item you want to buy, etc) that colors up/lights up proportionally with how much of its value you have set aside. That way, you can be even more motivated to “fill it up”.