ISM services data were released Thursday and slipped to a weaker than expected 48.7, an indication the service sector contracted last month.
A recovery has taken place in the manufacturing sector and the services sector will likely follow, Tilse said. "We'll see gradual improvement there in the next few months."
The unemployment rate may reach 10.5 percent by the first quarter of next year, John Lonski, Moody's Capital Markets chief economist, told "Squawk Box."
"Though companies may be firing… companies are not yet in a hiring mode," Lonski said, noting that there are lingering uncertainties about the strength of demand.
"The takeaway is that the monthly reduction in payrolls continues to narrow… that's good news, we're moving in the direction of stabilization of unemployment."
Jobs Recovery Taking Longer
Others, however, are not as optimistic. BNP Paribas cut its jobs forecast as a result of the ISM services data, and now expects a fall of 160,000 non farm payrolls for November.
Bankruptcies are still going on, especially for small and medium size enterprises, Hans Redeker, global head of foreign exchange strategy at BNP Paribas, told CNBC.
In past economic cycles, an economic rebound was indicated when small and medium size companies were doing better, but currently this is still far from happening, Redeker added.
"We've noticed that it's taking longer and longer and longer for the jobs lost in every recession to be recovered," Rob Carnell, chief international economist at ING, said.
There is still a "huge amount of spare capacity in the US economy," and employment may continue to fall into next year, Carnell said, but added that temporary jobs numbers are moving higher – that can be an early indicator that things are beginning to improve.
Joanne Collins, a strategist at Payden & Rygel agrees that unemployment has not yet peaked. "It's probably going to get close to 11 percent before it peaks out next year," Collins told "Worldwide Exchange."
But although Friday's figure could move stock markets to the downside if it disappoints, investors should also look at the monetary policy side of the equation. Historically, the Federal Reserve has not tightened monetary policy after recessions before employment picked up.
So the equity market needs some question mark regarding jobs, Tilse argued. Otherwise, if it is clear that unemployment is improving the Fed starts tightening.