So this is what 'full employment' looks like?

Obama: Americans anxious about economic future

For more than seven years, Federal Reserve officials have touted their progress toward achieving "full employment," with the most recent target a 4.9 percent unemployment rate.

With Friday's nonfarm payrolls report showing that the goal has been achieved, perhaps the Fed can raise the "Mission Accomplished" banner along with a welcome mat to the world of "full employment."

The jobless rate last reached this level in February 2008, following a run from June 2005 to April 2008 during which unemployment never eclipsed 5 percent. Getting a "4-handle" on the number — using Wall Street lingo — was supposed to represent jobs nirvana, the point at which the Fed finally would be able to declare victory and meaningfully begin to roll back its excessive easing programs that began in 2008.

But with the 5 percent goal line crossed, the jobs market remains a riddle. Consistent job creation has come with less robust gains in wages, and a seemingly positive report in most aspects was greeted with a strong sell-off on Wall Street.

In short, it was supposed to feel better than this.

Read More Jobs report eliminates some pessimism over economy

Government numbers "don't show the quality of the jobs. They don't obviously pick up the anxiety that workers are feeling," said Joseph LaVorgna, chief U.S. economist at Deutsche Bank. Concerns over job security, particularly about being displaced by technology disruptors, "may also be adding to economic jitters and uncertainties," he added. LaVorgna said he believes the economy actually is near full employment, though it doesn't seem that way to many in and out of the labor force.