Another sign of strength in the employment market: job cuts fell 27.6 percent to 36,594 in March from 50,579 in February, according to global outplacement consultancy Challenger, Gray & Christmas.

The numbers include payroll reductions announced by U.S.-based employers. The March total was the lowest since 32,640 in December.

To be sure, the March reading was 6.4 percent higher than 34,399 a year earlier, marking the fourth straight year-over-year increase.

Job cuts registered 140,214 for the first quarter, up 15.6 percent from a year earlier, with 47,610 directly attributable to plunging oil prices. Crude prices hit a six-year low last month.

“Without these oil-related cuts, we could have been looking one of lowest quarters for job-cutting since the mid-'90s when three-month tallies totaled fewer than 100,000," Challenger, Gray CEO John Challenger explains.

"However, the drop in the price of oil has taken a significant toll on oil field services, energy providers, pipelines and related manufacturing this year."

The tide might be turning, though. Only 1,279 job cuts were announced by energy firms in March, which is 92 percent fewer than the 16,000 announced in February.

Meanwhile, though many economists focused on the strong elements of the official February employment numbers, New York Times columnist Neil Irwin notes that in reality they're a mixed bag.

"The American job market has truly, really, finally, unquestionably shifted into a higher gear," he writes.

"On one hand, the results on job creation and the unemployment rate were about as good as one might hope for," Irwin explains.

The unemployment rate slipped to an almost-seven-year low of 5.5 percent. And non-farm payrolls rose 295,000, representing the 12th straight month with a gain of at least 200,000. That's the longest such streak since 1995.

But, "on the other hand, the lack of progress on wages and lack of progress in pulling people into the labor force give plenty of ammunition to those who believe that there remains plenty of slack in the labor market," Irwin notes.

Average hourly wages rose only 2 percent in the 12 months through February. And the labor participation rate totaled only 62.8 percent last month, barely above the 37-year low 62.7 percent.

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