Decide just how much "significant" is when the word is used to describe higher-than-expected project costs. A chat with your Prime Mover may be instructive on this point.
Begin with a careful examination of the critical path (that series of tasks and outcomes that, if prolonged/delayed, would require a postponement of the project result). In particular, look for (a) rookie participants, (b) unfamiliar work, (c) marginally reliable vendors and/or participants and/or (d) the convergence of two or more tasks in order to produce one milestone.
Either on your own (good) or with involved participants (much better), invest some time discussing the answer to three questions; (a) what could go wrong that would result in a delay?, (b) what would be the earliest warning sign that a delay was going to happen and (c) what would be the quickest, cheapest, best thing to do in the event of the delay? Elaborate the answers into a mutually understood 'Plan B'.
Ask key participants (people who are not easily replaced) who you should go to for help in the event they died or some even worse event threatened your project. (Just kidding). Explain that their contribution to the project and its deadline is so crucial that they are one of a small handful of people you're developing worst-case scenario contingency plans around. Try not to intimate that they could back out of the project because you've already got their replacement identified.