Stocks may now be on the path to new highs, though the journey will depend on whether the chill on the economy is purely from winter storms.
In her first congressional testimony as Fed chair, Janet Yellen on Tuesday convinced the markets that she is not an unknown quantity but a dovish voice very similar to former Fed Chairman Ben Bernanke. She said the Fed should continue to taper its quantitative easing program unless there is some notable change in the economy, and that the Fed plans to hold short-term rates low for a long time.
That reassurance and an announcement by Republicans that they would put the debt ceiling to a vote with no conditions triggered a powerful rally that drove the S&P 500 through key technical levels to 1,819, a gain of 1 percent.
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"The fact that we've punched back up through what I thought would have been [an S&P 500] mid-1700s trading range suggests the market is sniffing out something better than that," said Mark Luschini, chief investment strategist at Janney Montgomery. "That may be that a lot of attention going to the weather may actually be true. Janet Yellen's testimony did nothing to dissuade some people who view her as dovish."
But some technicians remain cautious and say that the market may not yet be firing on all cylinders.
"The Dow is the weakest of the indices," said Paul LaRosa, chief market technician at Maxim Group. "It's rallying up to resistance at 16,000. The other three are definitely stronger, but I would still treat this rally with a little caution."
The Dow closed at 15,994, a gain of 1.2 percent. The Nasdaq was up 1 percent at 4,191, higher on the year but still off its January highs.
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"If you're short, you've got a problem," said Dennis Gartman, publisher of the Gartman Letter. Gartman became neutral on stocks a couple of weeks ago but said that now he can't help but be long.
"The trend lines all held," he said, noting that the market is heading back toward its highs.
Art Cashin, director of floor operations at UBS, had been eyeing 1,800 as a key level the market needed to hold, but it jumped past it and lunged through 1,810, another key resistance zone around the 50-day moving average.
"I think this is setting you up for probably a shot at the old highs," he said. "That'll be the key test. Can we meet them and beat them, or do we roll over there?"
The S&P 500 reached a high of 1,850 in mid-January.
(Read more: Art Cashin: Wall St. liked it when Yellen said ...)
Market breadth does not necessarily signal a move higher, however, said MacNeil Curry, global head of technical strategy at Bank of America Merrill Lynch.
"My feeling is this is topping and rolling, and we should see a move down to the 200-day moving average," he said.
Seasonality is also a factor, Curry said, adding that February is not a particularly great month for stocks, but when January is negative, it is even worse and closes lower 63 percent of the time.
The number of stocks trading above their 200-day moving average had dropped below 60 percent, he said, and that "shows breadth deterioration, which is often what you see in a correction."
The 200-day moving average is 1,713, and the S&P reached a low of 1,737 in the recent 6.5 percent pullback from its mid-January high. If the S&P 500 does not back off as Curry expects, the market could be on track to challenge its highs.
"If we close above 1823, then things start to get more constructive," he said.
While stocks have rallied back in the last four sessions, Treasury yields have not risen much. The 10-year was at 2.72 percent Tuesday. "Basically, I think 10-year notes are still bullish," Curry said. He is watching a level of 2.54/2.40 for 10-year yields.
The Treasury auctions $24 billion in 10-year notes at 1 p.m. ET Wednesday. There is no data, but traders are already looking ahead to Thursday's retail sales to see what impact weather may have had on that important consumption number, though most of the activity is expected to bounce back.
(Read more: Yellen sees better economy, less money printing)
Yellen said in her testimony that it's too soon to determine if weather was behind the weak job reports for December and January. Economists say the unusually cold and snowy winter has already shaved several tenths off first-quarter GDP growth.
—By CNBC's Patti Domm. Follow her on Twitter