"Today's move (in oil) is a real positive for corporate profits," said Doug Cote, chief market strategist at Voya Investment Management.
Energy firms are expected to have the worst earnings decline as the sector suffered from the drastic decline in oil prices.
Stocks have remained in a range, with the S&P 500 roughly between 2,051 and 2,100.
Monday "had the characteristics of a shakeout, but we are not convinced that the pullback has fully matured yet," BTIG chief technical strategist Katie Stockton said in a note. "A breakout above intraday resistance near 2,080 by the S&P futures (2,089 for the SPX) would be an "all-clear" signal, in our view."
The S&P 500 touched a high of 2,089.81 in intraday trade on Tuesday and closed down 4.29 points, or 0.21 percent, at 2,076.33, with utilities leading eight sectors lower and energy and healthcare the only advancers.
The U.S. dollar traded 1 percent higher as the euro fell to $1.08. The U.S. 10-year Treasury yield edged lower to 1.88 percent.
"Today is a little bit of a day where crude oil and the dollar is what the market is going to focus on," said JJ Kinahan, chief strategist at TD Ameritrade. As "bond (yields) continue to move higher you may see people sell stock."
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He added that trade today and Wednesday morning will likely be slow as investors await Wednesday afternoon's release of the Federal Open Market Committee's meeting minutes.
Kinahan is looking at the minutes to show "where's the division and what the Fed members were pushing for."
Earlier, equities traded higher with the Dow Jones industrial average briefly adding 100 points.
Healthcare and energy helped the S&P 500, while the iShares Nasdaq Biotechnology ETF initially boosted the Nasdaq and ended nearly 1 percent higher. The Dow transports closed up about half a percent.
"We did have a good number that came on job openings. That took the pressure off people worrying about slow growth," said Bruce Bittles, chief investment strategist at R.W. Baird, noting that signs of moderate economic growth pushes out a Federal Reserve interest rate hike.
"I think the Fed raising rates in June is off the table and if the (economic) numbers improve then it comes back on the table for September," Bittles said.
The Job Openings and Labor Turnover Survey (JOLTS) showed 5.1 million job openings on the last business day of February, the highest since January 2001 but little changed from the prior month, the U.S. Bureau of Labor Statistics reported on Tuesday. The number of quits and hires declined slightly but were similar to January figures.
"Bottom line, the demand for labor in February was pretty good," Peter Boockvar, chief market analyst at The Lindsey Group said in a note, "but because the supply of labor has been more limited relative to this, we're seeing a continued drop in the unemployment rate."
The monthly non-farm payrolls report for March significantly missed expectations on Friday, but traders mostly digested the data as partly seasonal and as another weak indicator that could delay an interest rate hike.
"The market is taking bad news very well," said Jack Ablin, chief investment officer at BMO Private Bank. "We're in a period of bad news is good and good news is good, too. (Today's movement) seems more of a liquidity move ... (that is) more technical than fundamental."
Analysts expected a better monthly labor report based on declining weekly jobless claims. Lance Roberts, general partner at STA Wealth Management, said a reduction in first-time unemployment claims does not necessarily point to increased hiring or wage growth.
Firms will reach a point at which they have consolidated their workforce and aren't letting employees go, he said. "When I post a job opening that doesn't mean I'm hiring. I'm being very selective."
He added that the employment ratio for the 16 to 64 age group declined last month.
The only other economic report due was consumer credit, which showed an increase in February from the previous month.
"It's a very light day today in terms of economic news," Cardillo said. "The market's going nowhere. It's not breaking into new territory and it's not falling apart. I think investors should be cautious and defensive."
Earnings expected on Tuesday include Dave & Buster's after the bell. Alcoa posts results after the bell on Wednesday in the unofficial start to the earnings season.
Low oil and the strong dollar are expected to continue weighing on corporate profits. Consensus is for a 3 percent decline year-over-year for S&P 500 first quarter operating earnings, as of Friday data from S&P Capital IQ.
"Everybody's holding their breath to see what earnings look like," STA's Roberts said. "I think there's a lot of real concern now about the strength of earnings."
U.S. stocks closed higher on Monday, rebounding from initial losses on the disappointing jobs report Friday as it and other weak economic data gave investors renewed hopes of a delayed increase in rates.
"It just shows how sensitive the market is right now to expectations of Fed policy. The Fed wants to send the message it will be very careful how it proceeds from here," said Alan Skrainka, chief investment officer at Cornerstone Wealth Management. "The Fed has a clear signal to investors it will not... snuff out the recovery."
Minneapolis Fed President Narayana Kocherlakota said on Tuesday the Federal Reserve can wait until the second half of 2016 to start raising interest rates, and to then raise them gradually to just 2 percent by the end of 2017.
"In essence he lays out the case for the most dovish of the Fed," said Quincy Krosby, market strategist at Prudential Financial. "That's sneaking into the market. They believe it may be the case."
Greece remains an issue as the government leaders sought reparations from Germany for damages during the Nazi occupation of World War II. Germany's economy minister said the demand for 278.7 billion euros ($302 billion) was "stupid," Reuters reported.
Greek Prime Minister Alexis Tsipras is scheduled to meet with Russian leaders on Wednesday.
European equities ended sharply higher on Tuesday with receding fears over an impending rate hike in the United States.