I have seen a few todo apps that update their app badges at midnight, always showing the correct number of due tasks. They do this without the use of Push Notificat
Try this
[[UIApplication sharedApplication] setApplicationIconBadgeNumber:1];
To do this through local notifications you have to set the value in applicationIconBadgeNumber
UILocalNotification *localNotification = [[UILocalNotification alloc] init];
localNotification.applicationIconBadgeNumber = 1;// set here the value of badge