P2P systems exploit the uploading bandwidth of individual peers to distribute content at low server cost. While the P2P bandwidth sharing design is very efficient for bandwidth sensitive applications, it imposes a fundamental performance constraint for delay sensitive applications: the uploading bandwidth of a peer cannot be utilized to upload a piece of content until it completes the download of that content. This constraint sets up a limit on how fast a piece of content can be disseminated to all peers in a P2P system. In this paper, we theoretically study the impact of this inherent delay constraint and derive the minimum delay bounds for realtime P2P streaming systems. We show that the bandwidth heterogeneity among peers can be exploited to significantly improve the delay performance of all peers. We further propose a simple snow-ball streaming algorithm to approach the minimum delay bound in realtime P2P video streaming. Our analysis suggests that the proposed algorithm has better delay performance and more robust than existing tree-based streaming solutions. Insights brought forth by our study can be used to guide the design of new P2P systems with shorter startup delays.