When you say that you "probably" waited too long to let management know, that typically means that you definitely waited too long. Rather than looking for that graceful way out, you and your company will be far better served if you take the businesslike way out.
This means that you should go to management immediately and tell them what is going on. Bring all of your materials, data, and related communication, and show them precisely where you are. Let management see the true breadth of the project, and be sure that they can see the various approaches that you took, what worked and what failed, and the milestones that you met.
At the same time, remember that management is going to be interested not only in what caused the problem, but also in what to do from this point. Since you are most familiar with the realities of the project, you should try to develop an alternative strategy to get it completed. That's about as graceful as this awkward situation can be.
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