He expects to see 200,000 nonfarm payrolls added in December, and he said the unemployment rate could fall further.
"If it doesn't fall this month, I do expect it to fall quite sharply though the first half of this year, in part because of the expiration of the emergency unemployment insurance program," Zandi said. "That will shave 0.2 to 0.3 percent off unemployment itself, primarily because older workers who have been collecting unemployment insurance will retire."
The jobs report is also one of the most important metrics watched by the Fed when it considers the course of monetary policy.
Last month, the Fed decided to begin slowing its $85 billion monthly bond- buying program. It is reducing the program by $10 billion in January, and it's widely expected that the central bank will move to cut back on quantitative easing at a similar pace until it concludes by year-end.
"The FOMC minutes are going to give us insight into why they decided to do the token taper," said George Goncalves, Treasury strategist at Nomura Americas. "They definitely are focusing on something. Is it just the economy accelerating? Or are they worried about a little frothiness in the markets? It will be interesting to see why they tapered."
(Read more: Global stock funds mark record inflows for 2013)
Analysts say the employment report would have to be far off-target to influence the Fed.
"I think unless you get a really awful number—and it would have to accompany a lot of other bad economic reports for the Fed to do an about-face—the Fed will do exactly what it said it would do," said Randy Frederick, Charles Schwab managing director of active trading and derivatives. "It's going to start this month."
He thinks that it should be a bullish week for the stock market but sees a risk of turbulence in early February when Congress addresses the debt ceiling.
"The market doesn't go down just because it's up, there's got to be a catalyst," Frederick said, adding that he expects January to be positive for stocks—a good omen after last year's nearly 30 percent gain in the S&P 500.
John Stoltzfus, chief market strategist at Oppenheimer Asset Management, also sees a positive period for stocks but expects a correction before the S&P heads higher to rise above 2000 by year-end.
"We think the market at some point will have to take a breather—a pause to ponder," he said. "We think it tried to do that in the fourth quarter, but the good news, the economic data overwhelms whatever catalyst comes up that could send the market lower."
One area of possible concern stock traders will be monitoring in the coming week is the bond market. The yield on the 10-year ended 2013 at 3.03 percent, a two-and-a-half-year high, boosted by the Fed's move to unwind its easing program and by stronger data. It was at 2.99 percent late in the day Friday.
"There's been this eerie drift higher in rates, not too terribly different than the overall move higher in the stock indices into the end of the year, which has really placed yield levels at much more attractive points than they have been at in some time," Goncalves said.
This week could be the most interesting for the bond market until the week of the Fed's meeting Jan. 28 and 29 because of the jobs report, Fed minutes, and three auctions for $64 billion in 3-year and 10-year notes and 30-year bonds, he said.
The 10-year may not be bid aggressively, and yields could rise, Goncalves said. The jobs report may be a driver for bonds as well.
"If it's super strong, we're going to test 3.10 on the 10-year," he said. "Then if we break 3.10 ... it's going to be tough. It's going to dispel the notion that rates can find some footing."
Goncalves' expectation, however, is that the yield range trades up to 3.25 percent. The stock market has taken the 3 percent 10-year yield mostly in stride, but a more rapid move higher would be a concern.
(Read more: What matters after first trade of 2014)
While the Fed's plan to taper back its bond-buying has driven up rates at the long end, shorter-term rates are also rising. The Fed has attempted to thwart a move in the latter by stressing that it will hold its fed funds target rate at zero far into the future.
In a speech Friday to the American Economic Association, Bernanke emphasized that "tapering" the bond program is not tightening.
Short-term rates fell after the Fed failed to announce an expected tapering of QE in September, and the move continued up until the December Fed meeting.
"Two-thirds of that got unwound in the last two weeks of the year. Now the question is are they going to grind lower again," Goncalves said, adding that the market is challenging the Fed's campaign to keep short-term rates lower for longer. He said it is most apparent in the euro-dollar futures market.
"Everyone had all these high hopes it's going to work out great, that they're going to transition from QE to forward guidance," he said. "The bond market is not buying it."
The market is also watching the Fed transition and waiting for cues from Yellen on rate guidance.
"At least until Yellen starts, and she sets the agenda and gives us the metrics that she watches, until then we're in a transition period and we're going to focus on what the former Fed regime was looking at," Goncalves said. "If she's going to strengthen forward guidance, she's going to have to do a better job than Bernanke did."
Oil prices will also be of interest after the big 6 percent decline in West Texas Intermediate crude in the past week. WTI settled at $93.96, a one-month low, and a big decline from its recent high of $100.32 per barrel.
"I expect crude oil prices to remain under pressure as the market anticipates the return of Libyan oil to the market," said Andrew Lipow, president of Lipow Oil Associates. "And the U.S. refining industry will begin its spring maintenance season over the next couple of weeks, further reducing crude oil demand."
The winter storm that swept the Midwest and East Coast could also mean less fuel demand, as drivers stayed off the road Thursday and Friday, he said.
What to watch
10:00 a.m. ISM nonmanufacturing
10:00 a.m. Factory orders
Earnings: Micron, Apollo Group, The Container Store
8:30 a.m. Trade balance
8:30 a.m. Boston Fed President Eric Rosengren
1:00 p.m. $30 billion 3-year note auction
2:10 p.m. San Francisco Fed President John Williams
Earnings: Constellation Brands, Ruby Tuesday, Family Dollar, Monsanto
8:15 a.m. ADP
1:00 p.m. $21 billion 10-year note auction
2:00 p.m. FOMC minutes
3:00 p.m. Consumer credit
December chain store sales
Earnings: Alcoa, PriceSmart, Supervalu, Texas Industries
8:30 a.m. Jobless claims
1:00 p.m. $13 billion 30-year bond auction
1:30 p.m. Kansas City Fed President Esther George
8:00 p.m. Minneapolis Fed President Narayana Kocherlakota
8:30 a.m. Employment report
10:00 a.m. Wholesale trade
1:00 p.m. St. Louis Fed President James Bullard on economy
—By CNBC's Patti Domm. Follow here on Twitter