Economists expect that 180,000 jobs were added in January and that wages grew at a slightly higher annual pace of 2.6 percent.

The unemployment rate is expected to remain unchanged at 4.1 percent. But that average hourly wage number within the monthly jobs report has a chance to surprise the market, and it is the one number that could trigger a jump in already rising interest rates.

The pace of wage growth is expected to accelerate, with a 0.3 percent increase in January, after a similar gain in December, according to Thomson Reuters. The January employment report will be released at 8:30 a.m. ET Friday.

Bank of America Merrill Lynch economists are forecasting a 0.3 percent gain, due to minimum wage increases in 18 states and a number of cities, as well as corporate wage hikes. But some economists do not see as much impact and have lower estimates for wage growth.

"We included some of the upside risk to our number from the minimum wage increases that went into effect Jan. 1 and corporate pay raises from tax reform. Some [minimum wages] were only adjusted for inflation. Those would have modest impact, but others were larger," said Joseph Song, senior U.S. economist at Bank of America.

J.P. Morgan economists expect 200,000 jobs and a 4 percent unemployment rate, but they see just a 0.2 percent rise in wages. They said minimum wage gains should have just a modest impact on national data. They also note one-time bonuses, distributed by a number of companies because of tax reform, will not show up in the data.

Any sign of wage growth could fan already rising inflation expectations in the Treasury market, where yields have been rising fairly dramatically. Any sign of higher inflation could ramp up expectations that the Federal Reserve would raise interest rates more than the three hikes it has forecast for this year. On Wednesday, the Fed acknowledged increased expectations for inflation and strengthened its own language, suggesting that inflation will reach its target of 2 percent this year.

"The wage number is all that matters," said George Goncalves, head of fixed-income strategy at Nomura. "Maybe companies will now be able to pass through [tax savings] in wages to employees. This is suggesting inflation is more of an upside risk and rates are too low."

In the past week alone, the benchmark 10-year Treasury yield has jumped to 2.79 percent, from last Friday's 2.66 percent. That big move in rates influences a whole range of loans, including home mortgages. The rise in yields has also caused some anxiety in the stock market. The is down 1.8 percent for the week so far.

Stephen Stanley, chief economist at Amherst Pierpont, said he sees only a 0.2 percent gain in average hourly wages for January. "Typically, minimum wage changes have not been a huge thing," he said. "Typically they don't hit a high percentage of the workforce, but this has been an unusual circumstance because so many states and cities raised this year."

But Stanley does not see a big impact yet and expects wages to gradually rise this year. "I think we'll get to the 3 percent year-over-year on hourly earnings," he said.

Economists have been looking for wage growth to pick up, as the economy gets closer to full employment.

"I think part of the issue is productivity growth has been so low and firms aren't going to pay workers real wage increases when they're not seeing the marginal increase in productivity," said Stanley. He expects that to pick up, and an anticipated increase in corporate spending could help that.

Stanley sees payrolls increasing 170,000 in January, after December's disappointing 148,000 gain. He said he expects to see a slowdown in job growth throughout the year.

"I think probably they will be a little lower over the course of the year. It definitely seems we should be decelerating. We decelerated very marginally last year. I would expect we're probably going to be at 150,000 to 160,000 over the course of the year," he said. "If we were going to do better than that, that would suggest firms are finding ways to pull people out of the woodwork."

According to IHS Markit economists, 46 states were back at their pre-recession peak employment levels by the end of last year. Two states, Mississippi and New Mexico, will reach that in 2018, leaving just Connecticut and Wyoming behind.