Your final statement seems a bit contradictory to me. If the client can't hire employees for certain work, doesn't that increase their reliance on consultants (and reduce the chance you'll get cut)?
If a company has to cut costs they cut the positions they can do without, and in those positions consultants are cut out first.
Of course if you aren't easily replaceable or they actually need you then they won't cut you, but even then, if it really comes down to it consultants get cut before employees that are equally as important.