A prospective candidate elsewhere asked me about this, in light of the various financial pressures universities are under due to the Trump Administration's actions (many of which are illegal, but we'll see–Columbia's capitulation certainly didn't help). 

The only law schools that are fiscally autonomous are free-standing law schools (like Brooklyn Law School, for example).  Most law schools are part of universities, and almost all law schools send some of their tuition revenue to the university, even if they keep much of the revenue for law school operations.  But the relationship between the law school budget and the university budget varies school by school.  What we are seeing already, due to the NIH business, is universities taking across-the-board cost-cutting measures, some of which involve across-the-board hiring freezes.  That can affect law schools too.  (The Univeristy of California has imposed a system-wide hiring freeze, for example, which will affect the law schools at Berkeley, Los Angeles, Davis, and Irvine, and maybe also San Francisco.)  The effect has the potential to be most serious at schools that get a lot of NIH money (I expect the NSF to follow suit by the way on limiting indirect research costs):  those are the schools that may be staring at $100 million dollars-and-up holes in their budgets.  Under those circumstances, I would not be surprised to see universities wanting more of their law school’s tuition revenue and freezing hiring by all units.

So right now,  my prediction will be that next year’s law teaching market will be tighter than this year’s.  The only countervailing force is that there was a big uptick in law school applications this year (20% here, for example, and that is not atypical), and since almost all law schools depend on a steady stream of tuition revenue, this enables them to hire.