Still, traders are likely to remain cautious before key economic reports due later this week. The minutes from the Federal Reserve's last meeting of 2013 are due out on Wednesday and the December jobs report comes out Friday morning.
The health of the labor market will likely determine the pace of further reductions in bond buying by the Federal Reserve under new chair Janet Yellen.
Nearly 60% of the 30 investment strategists and money managers surveyed by CNNMoney believe the central bank will continue to gradually cut back on its bond purchases throughout this year so it can completely wind down its quantitative easing program by the end of 2014.
Despite Tuesday's healthy gains, 2014 has so far been a dud, especially in comparison to 2013. The Dow and S&P 500 ended the year at record highs and the Nasdaq finished at its highest level in over a decade.
As the market rallied, U.S. stock funds raked in a record $352 billion last year, breaking the previous record set in 2000, according to TrimTabs data.
Bond funds, on the other hand, lost a record $86 billion as investors pulled out in light of rising rates.