From the documentation of SQS, Max time delay we can configure for a message to hide from its consumers is 15 minutes - http://docs.aws.amazon.com/AWSSimpleQueueService/late
Untested. Perhaps publish to and SNS topic that has no SQS queues. When delivery needs to happen, subscribe the queue to the topic. (I've not done this, I'm not sure if this would work as expected)
Push messages as files to a central store (like S3). Create a worker that looks at the time created timestamp and decides whether to publish them to a queue or not. If created >= 1d ago, publish.