We study online mechanisms for preemptive scheduling with deadlines, with the goal of maximizing the total value of completed jobs. This problem is fundamental to deadline-aware cloud scheduling, but there are strong lower bounds even for the algorithmic problem without incentive constraints. However, these lower bounds can be circumvented under the natural assumption of deadline slackness, i.e., that there is a guaranteed lower bound s > 1 on the ratio between a job's size and the time window in which it can be executed. In this paper, we construct a truthful scheduling mechanism with a constant competitive ratio, given slackness s > 1. Furthermore, we show that if s is large enough then we can construct a mechanism that also satisfies a commitment property: it can be determined whether or not a job will finish, and the requisite payment if so, well in advance of each job's deadline. This is notable because, in practice, users with strict deadlines may find it unacceptable to discover only very close to their deadline that their job has been rejected.