With no economic data of note Tuesday, investors focused on speeches from Fed officials for early indication as to whether Bernanke's testimony will signify a reduction or end to monetary easing.
In a lecture in Germany, Bullard noted the U.S. should "Continue with the present quantitative easing program, adjusting the rate of purchases appropriately in view of incoming data on both real economic performance and inflation."
"He's traditionally rather hawkish," said one trader of Bullard. "He came out with some dovish comments espousing QE's asset purchase efficacy."
(Read More: What the Fed Misses: The Market Isn't the Economy)
Stocks got an added boost after Dudley said that the central bank should be prepared to change the pace of its bond-buying program as conditions warrant.
"I believe we should be prepared to adjust the total amount of purchases to that needed to deliver a substantial improvement in the labor market outlook in the context of price stability," Dudley said, adding, "In doing this, we might adjust the pace of purchases up or down as the labor market and inflation outlook changes in a material way."
But because of the uncertain economic outlook, "I cannot be sure which way—up or down—the next change will be," he added.
Market speculation about the tapering off of quantitative easing has grown over the past week, fueled by speeches from Fed hawks John Williams, Charles Plosser, and Chicago Fed President Charles Evans.
(Read More: QE Halt Would Be 'Too Violent' for Market: Fed's Fisher)
"We've had this huge dependence on QE over the course of the last three or four years," Stephen King, chief global economist at HSBC, told CNBC. "There's no doubt that financial assets have risen dramatically in value as a consequence of QE. I would argue financial markets become increasingly dependent on QE almost as a painkilling drug."
And that could lead to a pullback in stocks since fundamentals haven't kept up with the market rally, says UBS equity strategist Jonathan Golub. "It's all about the Fed and the pumping of liquidity," Golub told CNBC, "and when the market gets spooked on that" it's going to move lower. Golub has a 1,425 year-end target on the S&P 500, among the lowest on Wall Street.
Goldman Sachs strategists, meanwhile, raised their 2013 S&P 500 target to 1750, implying another 5 percent gain from current levels. The strategists base this increase not on earnings growth but multiple expansion.
"Reasons for P/E expansion include confidence in the medium-term outlook for U.S. economic growth and the wide gap between equity and persistently low bond yields that we assume will be closed more by stocks than bonds," the strategists wrote in a note.