A tightening labor market and rising inflation against a backdrop of slowing overall growth are painting an increasingly stagflationary picture for the U.S. economy. Stagflation, or conditions in which costs are rising but growth is not, last was seen in the 1970s, before then-Fed Chair Paul Volcker had to push the economy into recession to slay the inflation dragon. Now, with a variety of factors coming together to show inflationary-deflationary cross currents, Wall Street is bracing for another battle. Read More'Stagflation': Ghost of '70s could make return

"During the last year, as the economy has returned closer to full employment, the core cost structure of the U.S. economy has risen more aggressively and more broadly than ever before in this recovery," Jim Paulsen, chief investment strategist and economist at Wells Capital Management, said in a report for clients. "While the U.S. is not facing runaway inflation, the concept of stagflation (i.e., rising inflation rates combined with slower real economic activity) has become much more noticeable." Paulsen has been the Street's most emphatic messenger of the stagflation theme, contending for months that Fed policymakers are about to face a dilemma that will confound their efforts to raise interest rates and get monetary policy back on a normalized course.

Friday's nonfarm payroll report helped build the case.

The headline jobs number was solid if unspectacular, with 215,000 new jobs. But after pulling back in February, average hourly earnings gained 0.2 percent in March, good for 2.3 percent annualized growth. The two numbers show a push-pull effect in the economy that is bedeviling the Fed. "Overall, for the first time in this recovery, a broad and significant rise in core economic costs is slowing job creation, real consumer spending and profitability," Paulsen said. "In other words, stagflation is leaving tracks across the entire (economy)." While the jobs market continues to chug along, manufacturing is showing signs of slipping out of contraction, and the real estate data remain fairly strong. However, slowing exports and production have put the brakes on broader growth. Consequently, estimates of first-quarter gross domestic product growth have come down sharply. The Atlanta Fed had been forecasting growth as strong as 2.3 percent on March 11, only to slice the estimate all the way down to 0.6 percent earlier this week. "The main thing that's happening in the U.S. economy right now is a negative supply shock. The combination of retirement of baby boomers and historically low productivity growth is really limiting the supply side of the economy," Gad Levanon, chief North America economist for The Conference Board, said in an interview. "The demand side is starting to bump into supply constraints. That has the potential for creating some stagflationary forces."

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