"I wouldn't make it any more than a 50/50 chance," said Art Cashin, director of floor operations at UBS. "It's tough to say. Next week is seasonally for the better. I think you pulled some of the seasonality ahead with this strong postelection rally."
Cashin said a lot could depend on oil, which was above $53 per barrel late Friday.
"I think things are intact for an end-of-year push. It just didn't have enough power and volume to get that extra push," Scott Redler, partner with T3Live.com, said. He does expect the Dow to gather enough momentum to break the 20,000 level, and the market's consolidation in the past two weeks has been healthy.
"I think it's interesting biotechs showed some relative strength [Friday]," he said. "It'll help the whole theme of rotation, where money is moving around to keep the market going. There aren't that many dogs of the Dow, so if the bios, which have been weaker, start to act better, it would probably be a place to outperform in the beginning of January."
According to Stock Trader's Almanac, the Santa Claus rally falls on the seven-day period spanning the last five trading days of the old year and the first two trading days after New Year's. That would be between Dec. 23 and Jan. 4 this year.
The S&P 500 sees an average gain of 1.4 percent in the seven-day period, and if the market fails to rally it could be the precursor to a bear market or a bigger sell-off, the Almanac notes. It also points out that last year, there was no rally and the S&P 500 fell 5.1 percent in January before bottoming in February.
"The psychology seems to be setting up for a little bit of upward movement, not some strong 5 percent move. I think we could see a slow rise over the course of the rest of the year," said Don Townswick, head of equities at Conning. He also expects the Dow to break 20,000 in the coming week, but whether it holds is another thing.
Townswick said reality could set in with the new year, and investors will watch to see how swiftly President-elect Donald Trump and the new Congress will move on tax cuts, regulatory reform and promised fiscal spending.
Cashin said traders are already beginning to focus on some of the concerns about the Trump administration, even if U.S. markets have not reacted. His appointment this past week of outspoken China critic Peter Navarro to a new trade position stirred up a lot of chatter about whether Trump would take on China and others with tariffs or other trade-related actions.
"Before the election, we saw a lot of sideways markets because of the uncertainty. Uncertainty about all of 2017 starts to creep into peoples' minds as soon as they're done drinking their eggnog," said Townswick. But if there is a market pullback in the first quarter, he does not expect it to be major.
"I don't think it will go down a ton, but I think next year's results will depend a lot more on politics," he said.
Townswick doesn't expect any extreme action from the new administration. "These guys are all deal makers … deal-makers don't tend to want to go down in flames. They want to make deals and get to somewhere. I'm hoping these guys are going to get somewhere where everyone can win a little bit," he said.
Boris Rjavinski, Wells Fargo rate strategist, said pension funds could be a factor for the markets at year end.
"We're looking for something like $32 billion in outflows from domestic equities and $20 billion inflow into bonds. We think besides buying bonds, pensions would also be buying emerging market equities," he said. He said pensions need to rebalance their holdings, after the strong performance of U.S. stocks since the election and the weak performance in bonds.
"We're probably seeing some of these pension reallocations flows going through right now, and we might see them for a couple days at the start of next week," he said.
The S&P 500 ended the week up 0.3 percent at 2,263, while the Dow was up 0.5 percent at 19,933.
The 10-year Treasury note was yielding 2.54 percent Friday afternoon, and Rjavinski said he forecasts it could be just where it is now when next year ends.