"There's a sense that some momentum was building at the end of last year," Silver said, noting that if the December employment report comes in as expected, job growth would be at 200,000 for three straight months and four of the past five months.
Meanwhile, small-business hiring, a major engine of the job market, appears to be improving. The National Federation of Independent Business said its survey of small-business owners showed companies increased employment in December by an average of 0.24 workers per company, the best reading since February 2006.
(Watch this: Cashin: this jobs number could hurt stocks)
Eric Fisk, president of the 40-year Fisk Alloy, in Hawthorne, N.J., foresees a pickup in business this year, and he expects to expand his 175-person workforce by about 10 percent.
"A general statement—I would concur the overall tenor of business is quietly getting stronger," said Fisk, whose company makes high-quality alloy wire for conductor and connector products. "We'd been flat for the last couple of years."
An initial rebound in his business after the downturn of 2008 and 2009 went flat, he said, adding that Fisk Alloy is tied more to products than to the general business cycle.
Fisk sees other companies with improving outlooks, as well.
"The good ones keep getting better, and the marginal ones take a long time to die," he said. "The good ones are building inertia."
Fisk said he has been able to find and hire machine operators, but that some higher-level engineering positions are harder to fill.
According to Mesirow Financial economist Diane Swonk, the jobs market may have turned some months ago, but the government shutdown in October clouded the data.
(Read more: Stronger jobs report seen encouraging Fed taper)
"It's the trend in employment that matters, and the trends have been good," Swonk said. "What matters to me is not the number but also that the revisions have been good. In an economy you tend to miss stuff over time. You miss turning points. These numbers aren't very good at picking up turning points. They only catch it in the revisions."
She expects the report to show a mix of new jobs in construction and manufacturing.
"We could easily be surprised on the upside. Bottom line, if we keep turning out 200,000 jobs and up, that's enough to keep bringing people in," Swonk said. "The real test will be the participation rate and what it does in 2014."
The participation rate was reported at 63 percent in November, a 35-plus-year low but slightly above the October reading of 62.8 percent. From 2003 to 2007, it was closer to 66 percent. The rate reflects the number of Americans working or actively looking for jobs, and Swonk doesn't expect much change immediately.
She sees signs of the economy picking up steam.
"The last two quarters of the year could be the best two quarters back-to-back since 2005, and that was before the trade data," Swonk said. "Growth easily exceeded 3.5 percent. At first we thought it was an inventory fluke—it was more than a fluke."
Third-quarter GDP growth has been revised to 4.1 percent. Fourth-quarter GDP will be reported Jan. 30.
"I don't know if we're going to see this kind of growth sustaining," Silver said. "With less fiscal drag on the horizon, I think we are relatively upbeat about next year."
JPMorgan expects fourth-quarter 2013 growth of 2.5 percent and growth of 2.8 percent in 2014.
—By CNBC's Patti Domm. Follow her on Twitter