The same way they have always adapted - by learning to leverage big data better than their clients. Many if not all the top consultancies have invested heavily in big data over the last few years, and many if not all of their clients have more data than they know what to do with.
By the way - before 'Big Data', we had 'CRM'; even before, we had 'personal computers' or whatever... there is always something new. Big Data will be just one more opportunity: as business becomes more complex, you could argue the need for consultants keeps increasing. BCG for example has grown by 15% CAGR since 1990 and that growth rate has increased recently if anything.
PS: I am not a consultant anymore, so have no personal incentive one way or the other. This is just my (hopefully educated) opinion!