The idea of the Fed paring back on its bond purchases was also advanced after the Congressional Budget Office released estimates for a smaller-than-expected deficit this year of $642 billion, $200 billion less than its previous forecast. The Treasury has already indicated that it may decide in the next several months to issue less debt. Bernanke is expected to speak on the economic outlook before the committee Wednesday morning, but traders expect him to also discuss policy.
Crescenzi said he expects that when the Fed does trim its purchases, it will do so slowly to about $50 billion or $60 billion a month.
"That would still represent fairly substantial easing on an ongoing basis," Crescenzi said. "That's equivalent to about a half-point cut in the Fed-funds rate," he said.
The Fed will likely wait for several months of improved employment numbers before moving to taper, Crescenzi said. "We wouldn't put a high likelihood on tapering June 19, but it's not implausible. There's a scenario where it could happen. If payrolls are stronger, very vigorous and the full report is robust," he said. The next employment report is released June 7, and the Fed meets June 19.
Some analysts say the Fed's tapering of bond purchases should not be a big mover of markets, but the time will come, still several years away, when the Fed increases the Fed funds rate, and that will have an impact.
"If the Fed begins tapering, I don't think it makes a difference," said Dan Greenhaus, chief global strategist at BTIG. "The fact the stock market is higher only because of the Fed I don't agree with. If the budget deficit gets smaller and the economy improves, quantitative easing should be able to get smaller without some macroeconomic disturbance."
Greenhaus expects the Fed to start paring back in the third quarter and end its QE program about a year later.
The Fed has given itself an out if paring back the program hurts the economy. In its last meeting statement, it said it could either increase or decrease the amount of assets it is buying. With the Fed buying Treasurys, it has helped keep rates low but also pushed buyers into riskier assets, adding big support for the stock market.
"If the Fed tapers because the economy is improving, because the jobs numbers are better that would steepen the yield curve, and push yields up across the curve," Crescenzi said. "If it tapers because of costs and risks and it's worried about excess speculation, then it would be cutting off the fuel too soon, and the engine could stall for the economy."
Stocks hiccupped this week when the San Francisco Fed's Williams Thursday said tapering could come this summer, but for the most part, the market steadily moved higher. The Dow was down 42 points Thursday, but for the week, it is up 1.6 percent to a new high of 15,354. The S&P 500 was up 2 percent at 1667. The dollar index was up 1.3 percent, and the 10-year yieldended the week at 1.94 percent.
Andrew Burkly, head of institutional portfolio strategy at Oppenheimer Asset Management, said the market is overbought but could keep going up for now, with cyclical sectors driving it.
(Read More: JPMorgan Goes All-In on Rally; Sees Surge Growing)
"They were the laggards and now they are catching up," he said. Financials were the best performers of the week, up 3.7 percent, followed by industrials, up 2.2 percent. The telecom and utilities sectors, which led the market higher earlier in the year, were the week's laggards, up 0.4 and 1 percent respectively.
Greenhaus said he expects the stock market can continue to move higher, but it's showing signs of wear. "What gives me pause is the fact that the S&P is 12 percent away from its 200-day moving average. That's a stretched valuation," he said.
What Else to Watch
Housing data dominates the economic calendar in the coming week with existing home sales Wednesday and new home sales Thursday. Manufacturing PMI for Europe, the U.S. and China is released Thursday.
There are still a few late quarter earnings reports, including Hewlett-Packard, Toll Brothers, and retailers - Home Depot, Lowe's, Target, TJX and Saks.
The U.S.Treasury also auctions $99 billion in 2-year, 5-year and 7-year notes Tuesday through Thursday.
(Read More: What to Watch in Retail Earnings Next Week)