Financial markets have been locked in debate about how and when the Fed will back away from its $85 billion monthly bond-purchase program, or quantitative easing. The debate took shape as Fed officials this month voiced their varied views on when it should happen, with the most hawkish pushing for June. But Fed Chairman Ben Bernanke woke the market to the possibility the Fed could be ready to start "tapering," or cutting back on its purchases in the next couple of months, depending on the economy's progress.
Even though that same view was expressed earlier by New York Fed President William Dudley, the comment from the Fed chairman before a congressional committee sent markets on a rollercoaster Wednesday.
By Thursday, reports of the contraction in China PMI for the first time in seven month sent markets tumbling in Asia and Europe.
(Read More: Outlook for China's Economy Just Keeps Getting Worse)
That report also hit oil and industrial metals, like copper, hard, but they recovered losses along with U.S. stocks as the trading day progressed.
Stocks are up more than 16 percent for the year and are at an important crossroad where the market can act spooked by what not too long ago was construed as good news. Nuveen Asset Management Chief Equities Strategist Bob Doll said the current state of the economy is just right for stocks and should keep them moving higher until the economy looks too good, or robust.
"It doesn't last forever, but it goes until it doesn't anymore," said Doll. "My view is let's not try to make something too complicated. Let's recognize that the economy is improving fast enough for stocks to be satisfied but slow enough that the Fed stays dovish."
Even if the Fed tapers its bond purchases, that doesn't mean it ends the program or that it will start selling the $3.339 trillion in mortgages and Treasurys it holds on its ballooning balance sheet.
James Paulsen, a long-time bull, said the current environment is making him a little cautious. The Wells Capital Management strategist said an improving economy could keep rates moving higher, and that could pressure stocks. The 10-year note broke above 2 percent this past week for the first time since March.
Paulsen, too, is watching claims data, after the past week's claims fell by 23,000 to 340,000, and the continuing claims declined by 112,000 to 2.9 million during the week ending May 11, in the largest decline in more than a year and the lowest level since before the financial crisis. The claims are for the week ending May 18, which is the survey week for the May employment report. Economists were watching them closely, and JPMorgan economists said while they expect payroll growth to be slower in the second quarter than first quarter because of fiscal tightening, the claims are indicating the weakness in labor might not be that severe.
(Read More: Finally, Clarity From the Fed! Or Maybe Not ...)
"If claims keep falling toward 300,000, QE is over," said Paulsen. "I just think if you get a (monthly jobs) number closing in on 200,000 again, I think the discussion within the Fed will definitely go toward tapering. I think it's very encouraging that the Depression scaredy-cat Fed is actually starting to talk about normalizing policy. … I think China is a more frightening thing. I'd like to see them regain footing. I'm not sure the market is really that worried about the Fed going away from QE. There's been more discussion this year about the Fed tapering QE than at any other point."
Paulsen said he still expects the market to move a bit higher, but it should be more of a sideways move for much of the second half of the year, consolidating before moving higher later.
"The Chinese economy is an issue. I think the global recovery can go on without Europe. It can go on without Japan. It could conceivably go on without the United States, but it cannot go on without the emerging world," he said, adding China is in the process of adjusting to a slower growth rate. "I'm not over the top on it because I think there's growth in other parts of the world, but it's a little concerning."
But U.S. growth is improving and that should help stocks. Paulsen doesn't buy that it's the Fed that's pushed up the market, in contrast to other analysts and traders.
"Stocks are going to have a hard time for the rest of the year because bond yields are going to keep rising," he said. "I think that people are underestimating economic growth and sustainability. It's going to be hard for this thing to fall if we're going to grow closer to 3 than 2 percent for the second half."
Many analysts had expected a "Sell in May" market this year, since that had been the pattern of the last several years, and they had expected the economy to be pressured by sequestration and other federal budget cuts. While manufacturing data is running soft, the impact so far has not been as bad as some expected. Housing has been a bright spot, with existing home sales continuing to improve in April to the highest level in 3 1/2 years.
Doll also sees the improving economy lifting stocks, but with help from the Fed. "It's far more than the Fed. The economy is improving. We have modest improvement, modest earnings growth. We're not going to get a robust economy. That's precisely the good news for the stock market. My view is an acceptable economy is best for the stock market. If you get a strong economy, the Fed will disappear and we'll get inflation. Right now, we're in the sweet spot," he said.
What Else to Watch
Stock traders will also be watching bonds in the coming week, as the Treasury auctions $99 billion in two-year, five-year and seven-year notes Tuesday through Thursday.
"Given the sharp rise in yields, we would expect they'll be well-subscribed. May is a unique month. There's usually a bid for index buying," Goncalves of Nomura Americas said.
Rates can go higher, he said, but not much without more proof that the economy is improving. "Rates won't go higher just because the Fed stops. If the Fed stops too early, rates will go lower," he said.
Paulsen said rising rates could slow stocks as they adjust, but will not stop the market from going higher. He said based on history, it would take a level above 4 percent to stop stocks from rising.
The Week Ahead
Memorial Day; U.S. Markets Closed
9:00 am: S&P/Case-Shiller home price data
10:00 am: Consumer confidence
10:00 am: Richmond Fed
10:30 am: Dallas Fed
1:00 pm: $35 billion two-year note auction
1:00 pm: $35 billion five-year note auction
8:30 am: Weekly jobless claims
8:30 am: Real first-quarter GDP (second)
1:00 pm: $29 billion seven-year note auction
8:30 am: Personal income
9:45 am: Chicago PMI
9:55 am: Consumer sentiment