The Heritage Foundation article that you source states:
On the facts, it is true that real wages have been "stagnant" for the last year or so, but only in the sense that they remain high and have not declined.
Looking at the above graph, this statement appears to be pretty much true. Real wages have been stagnant for about two years but are far above their January 1996 level. This view changes, however, if you take a longer view. The following graph displays all the data available from the BLS website:
As you can see, real wages peaked in the early seventies and plunged in the late seventies and early eighties. They continued to decline and reached a low in about 1995. They are currently about where they were in 1967.
In any case, you can see the data for this and a number of other BLS statistics from the payroll and household surveys at http://home.att.net/~rdavis2/jobs.html. If you want to see just the graphs, they're at http://home.att.net/~rdavis2/jobgrafs.html.
As you can see, real wages peaked in the early seventies and plunged in the late seventies and early eighties. They continued to decline and reached a low in about 1995. They are currently about where they were in 1967. If 10,000,000 illegals enter the country and make $4 an hour, what impact does that have on average hourly earnings?
As usual you do some really nice charts. I think the weak dollar must be a killer on real wages. The early 70's were marked by the collapse of the Bretton Woods system and a devalued dollar. Carter ran an extremely weak dollar policy. Reagan had one during his second term. In contrast Clinton had a very strong dollar policy that started in 1995. Interestingly 1996 is when Greenspan gave his "irrational exuberance" speech. Exuberance yes, irrational no.
I wonder where real wages and our economy would be if the misconception that full employment is the worst fate mankind could face wasn't held as a universal, but unsupported truth.