(Read more: Obama: 'I Still Think We Can Get This Done')
Art Hogan of Lazard Capital Markets expects a deal in early January, but he says it will be important for Congress and the White House to show they are working together in the coming week. "Showing they're trying has stabilized this market," he said. "Every time we have constructive conversations, the market applauds that. At the end of the day, the market wants to see something substantive. An example of that was the celebration we had for two days when Obama went to $400,000."
House Speaker John Boehner countered Obama's proposal with a$1 million threshold, but on Thursday he could not get enough support in the House to vote on that plan, which the White House had already opposed. So,there is a seemingly great divide to overcome in the next few days.
Obama late Friday asked that Congress return next week to consider a scaled back plan that would prevent taxes from going up on all but the top two percent. Obama said he was still committed to a comprehensive deal on spending cuts and growth but sees little time left to get a bigger deal done this year while avoiding the fiscal cliff.
(Read More: Pros' Picks as 'Fiscal Cliff' Deal Nears)
"It could be very volatile on low volume which is scary. We've had triple-digit moves of late which have been directly correlated to our perception of what's going on in Washington," said Hogan. "You probably could double that move in thinner trade."
Stocks were higher in the past week in volatile trading,even with Friday's decline. The Dow was up 0.4 percent for the week to 13,190,and the S&P 500 was up 1.2 percent at 1430. The Nasdaq jumped 1.7 percent to 3021.
The House returns to work Thursday, but markets will be looking for headlines ahead of that on how discussions are going between the White House and Congress.
Besides "cliff" headlines, there are several economic reports in the coming week that should show continued improvement, particularly in housing with home-price data Wednesday and new-home sales Thursday.
The economy has been showing signs of improvement with surprises in a number of reports this past week. Home sales, for instance, rose 5.9 percent in November, to a three-year high, and durable goods jumped a surprise 2.7 percent, for a second month of gains. Consumer spending rose 0.6 percent, the most in three years.
(Read more: Pimco's El-Erian: Ugh, Recession Is Now More Likely)
"What's surprising was consumer spending was actually picking up in the fourth quarter. That was the message of today's data.Business spending was also picking up. The problem is the economy is still vulnerable to the fiscal cliff," said Barclays chief U.S. economist Dean Maki on "Closing Bell."
"Tax rates are going to jump significantly Jan. 1 if nothing is done quickly and that would cause, we think if it lasted, a contraction in the first quarter," Maki said. He added he is not expecting a recession. "We still think some deal will be reached over the next couple of weeks, and in that scenario we think the economy is going to grow 1.5 to 2 percent I the first half of the year. The risk of no deal is rising but we still think that will happen."
Stock market closes at 1 p.m.
0700 am Mortgage applications
0900 am S&P/Case-Shiller home prices
1000 am Richmond Fed manufacturing index
0830 am Jobless claims
1000 am New home sales
1000 am Consumer confidence
1100 am Oil inventories
1100 am Kansas City Fed survey
0430 pm Fed balance sheet/money supply
0945 am Chicago PMI
1000 am Pending home sales
1030 am Natural gas inventories