Most existing real-time protocols for sensor data dissemination use packet scheduling schemes to prioritize packets according to their deadlines. However, packet prioritization by itself cannot completely support real-time data dissemination requirements. In this paper, we propose new Just-in-Time Scheduling (JiTS) algorithms that take advantage of the available slack, if any, to reduce contentions and improve real-time performance by judiciously delaying packets as long as their deadlines are not missed. Specifically, we explore several policies for allocating the slack among multiple hops, including a non-linear policy where packets are non-uniformly delayed at intermediate nodes to account for expected higher contentions as packets get closer to the sink(s). Notably, our JiTS policies require neither lower layer support nor synchronization among sensor nodes making for an easy deployment. In our simulation study, JiTS significantly improves the deadline miss ratio and packet drop ratio compared to existing approaches in various situations. It is also shown that the Geographic Forwarding often used for real-time data dissemination substantially underperforms the Shortest Path routing especially when the load is high.