Economic news also supported stocks Tuesday. Consumer confidence for December came in at 113.7, its highest since August 2001 and up from an upwardly revised 109.4 read in November.
"I think consumer confidence was OK," said Peter Coleman, head trader at Convergex.
"There's not a lot of institutional participation going on this morning. ... There's not a lot driving it right now," he said.
The Richmond Fed current conditions manufacturing index rose to 8 points this month from 4 points in November. The Dallas Fed said that its production index, a key measure of state manufacturing conditions, rose to 13.8 points in December from 8.8 in November.
Ahead of the open, the S&P/Case-Shiller U.S. National Home Price Index — which measures all nine U.S. census divisions — rose 5.6 percent in October from the previous year, extending a new high from the previous month.
The Treasury Department auctioned $26 billion in 2-year notes at a high yield of 1.28 percent. The bid-to-cover ratio, an indicator of demand, was 2.44, the weakest since Christmas 2008.
Treasury yields were higher, with the 10-year yield near 2.56 percent and the 2-year yield around 1.23 percent.
"Small move. Zero conviction behind it as one might expect for a post-holiday trading session," said Guy LeBas, chief fixed income strategist at Janney Montgomery Scott.
"Today's economic data was generally stock friendly, a little bond unfriendly," he said. "Consumer optimism has been largely baked in. The question (is) whether it will translate into actual spending."
The U.S. dollar index traded little changed, with the euro around $1.046 and the yen near 117.44 yen versus the greenback in the close.
WTI settled up 88 cents, or 1.66 percent, at $53.90 a barrel as traders anticipated tighter supply. The first output cut deal between OPEC and non-OPEC producers in 15 years is set to take effect Sunday.
U.S. markets were closed Monday in observance of the Christmas Day holiday, and are closed again next Monday to commemorate New Year's Day. Last Friday, the Dow Jones industrial average posted its first seven-week win streak in two years and was within 70 points of breaking the psychologically key 20,000 mark.
Tuesday marked the second trading day in the so-called Santa Claus Rally period, which runs this year from Dec. 23, 2016, to Jan. 4, 2017. The S&P 500 usually rises 1.4 percent in that seven-day period around the end of the year, according to the "Stock Trader's Almanac."
"The market is on momentum roll. It has been for some time," said Peter Cardillo, chief market economist at First Standard Financial. "That stride hasn't been broken. It's just slowed down."
Overseas, the Nikkei 225 ended a touch higher while the Shanghai composite closed a quarter percent lower. The STOXX Europe 600 ended slightly higher.