Empowered by today's rich tools for media generation and distribution, and the convenient Internet access, streaming crowdsourced multimedia content (crowdsourced streaming, in brief) generalizes the single-source streaming paradigm by including massive contributors for a video/data channel. It calls a joint optimization along the path from crowdsourcers, through streaming servers, to the end-users to minimize the overall latency. The dynamics of the video sources, together with the globalized request demands and the high computation demand from each sourcer, make crowdsourced live streaming challenging even with powerful support from modern cloud computing. In this paper, we present a generic framework that facilitates a cost-effective cloud service for crowdsourced live streaming. Through adaptively leasing, the cloud servers can be provisioned in a fine granularity to accommodate geo-distributed video crowdsourcers. We present an optimal solution to deal with service migration among cloud instances of diverse lease prices. It also addresses the location impact to the streaming quality. To understand the performance of the proposed strategies in the real world, we have built a prototype system running over the planetlab and the Amazon/Microsoft Cloud. Our extensive experiments demonstrate that the effectiveness of our solution in terms of deployment cost and streaming quality.