Wednesday's rally will need to continue Thursday and into the end of the week before many analysts find more confidence that the stock market is firmly on its way upward.
"The bulls and bears are fishing for positions as we head into the September Fed meeting," said David Schiegoleit, managing director of investments at U.S. Bank Private Client Reserve.
"The bears may want to retest those lows before we get (to a fourth-quarter rally)," he said.
He's keeping an eye on the Challenger Gray job cut report at 7:30 a.m. ET, and the natural gas inventories at 10:30 a.m.
"Other than that we're really holding our breath until Friday's jobs numbers," Schiegoleit said.
Other data on tap include weekly jobless claims at 8:30 a.m. and the ISM nonmanufacturing index at 10:00 a.m.
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The number of bulls fell to just 1 percent above that of bears, for the fewest number of bulls since March 2009, according Investors Intelligence's advisor sentiment survey.
More bears could indicate fewer sellers and a higher trajectory for stocks going forward.
"It's a good time to be a buyer of risk," said Eddie Perkin, chief equity investment officer at Eaton Vance. "As an investor, you have to lean in and buy things that are on sale when there's fear in the market."
One of the areas he's looking into is large-cap tech stocks.
Robert Pavlik, chief market strategist at Boston Private Wealth, said he's still hearing too much talk of people wanting to get back into the market to make him comfortable.
"That's a good sign, but that's not the entire market," he said of the advisor survey.
"When ... I hear all the people who have clamored about going back in, that says to me we're not completely washed out yet, that there could be some pressure later on," Pavlik said. "I wish people weren't so confident that we're going to snap back right away."
Like U.S. Bank's Schiegoleit, Pavlik expects more selling pressure before a year-end rally.
Jack Ablin, chief investment officer of BMO Private Bank, would also like to see "more bearish investors."
"I think there's a little more vulnerability left," he said.
U.S. stocks will have less overseas news to digest Thursday. Both the Hong Kong and mainland Chinese exchanges are closed for a public holiday to commemorate the 70th anniversary of the end of World War II.
As a result, markets recently roiled by fears of a China slowdown could take a greater cue from fluctuations in oil prices.
Crude oil dipped more than 4 percent on greater-than-expected crude inventories before settling 1.85 percent higher at $46.25 a barrel. Natural gas inventory data out Thursday could add further volatility.
With "the lack of market data coming out of Asia over the next few days, we might see greater correlation with energy prices," Schiegoleit said, noting that oil is the third major factor for stocks, after data and the Fed.
"We don't see a whole lot of reasons for oil prices to trade higher but we see a lot of reasons for oil to trade lower," he said.
To be sure, the major intraday moves could be more noise as traders attempt to parse different signals on energy production and demand.
"In a volatile commodity market, it's going to be difficult to look at the day to day," said Art Hogan, chief market strategist at Wunderlich Securities.
Investors will also eye headlines out of Europe. The European Central Bank's governing council convenes a monetary policy meeting in Frankfurt on Thursday and is scheduled to hold a new conference at 2:30 p.m. (8:30 a.m. ET).
Many analysts said they are interested in President Mario Draghi's comments on economic growth in Europe and the impact from China. However, they don't expect major action from the ECB so close to a potentially historical move from the U.S. Federal Reserve.
The major averages rallied more than 1.5 percent at the close Wednesday to end near session highs, with the composite outperforming with gains of 2.46 percent to pull out of correction territory at 4,749.
The S&P 500 also closed higher, out of correction territory, up 1.83 percent at 1,948. The remained in correction. The blue chip index ended three straight days of losses with a gain of 293 points to 16,351.
Wednesday's gains mark continued volatility in stocks.
With the Dow's rise Wednesday, 10 out of 11 sessions have been triple-digit moves for the index, a streak last seen in 2013, when markets sold off on fears of decreased Fed stimulus.
The Nasdaq has also moved more than 2 percent in 7 of the last 10 sessions.
—CNBC's Gina Francolla and Robert Hum contributed to this report.
Correction: The job cut report is from Challenger Gray. The name of the firm was misstated in an earlier version.