I think the key phrase you mentioned Chip is that "communicate the state of affairs accurately to your client". Because, even when you try to leave a client and you have not properly elaborated the reasons why then they can always shift the failure of the project on you and that gives a bad rap for your consulting business.
Organizing a meeting with them to clearly state what's going on and where they are not supporting you would definitely open their eyes as long as the key stakeholders are there in the meeting. From that point on, they would do one of two things - (1) help you exit and find a replacement or (2) help you help them fix what they didn't support you with in the first place.
Either way, honesty and integrity are the keywords; hiding or going MIA never plays well
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