While inflation is quiescent now, with consumer prices rising only 1.5 percent in the year through March, it will ultimately accelerate, some economists say.

The recent increase in hiring will put upward pressure on prices, says Deutsche Bank senior U.S. economist Carl Riccadonna. Non-farm payrolls have risen for three straight months, gaining 288,000 in April.

"We know we crossed above trend growth toward the end of last year," he tells CNBC. "And inflation tends to lag by about six quarters, so toward the end of the year we will see inflation pressures start to tick up."

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At that point the unemployment rate, which stood at 6.3 percent in April, will probably be around 5.5 percent, Riccadonna notes. "That will lead to meaningful inflation pressures as well. . . . We're going into a period when there are going to be persistent upward inflation pressures."

Peter Boockvar, chief market analyst at the Lindsey Group, says rising rent payments will boost inflation. "With 35 percent of the population renting — the highest since 1995 — rents are very important," he tells CNBC.

Analysts at Capital Economics say rent around the country may rise up to 4 percent in 2014, compared with 2.8 percent last year, according to The New York Times.

The 0.2 percent increase in March consumer prices signals that inflation is headed higher, some economists say. "The overall picture is that inflation has stopped falling and is on a gradual uptrend,” Thomas Costerg, an economist at Standard Chartered, tells Bloomberg.

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