This divide among economists is also playing out in the markets, and Paulsen said the Fed is responsible for a backdrop of volatility. He also said the central bank should move just to preserve its credibility.
"They made this mess ... if there's volatility because of it, it's already a reflection of the Fed overwaiting. ... You think if you push this forward two or three months, Wall Street won't do the same thing again? Every time it comes up, Wall Street is going to react. It's kind of self-created volatility," he said.
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Peter Boockvar, chief market analyst at The Lindsey Group, said the Fed could drive stocks immediately higher with its actions, whether it hikes or not.
"My sense is nothing happens until 2 o'clock Thursday, and I think if they hike and sound very dovish, or if they don't hike, in those two hours we could have a good rally. If they don't hike, we'll have a bigger rally," said Boockvar.
What is less clear, however, is what happens the next day after the Fed's 2 p.m. statement Thursday and its 2:30 p.m. ET news briefing. "If they don't hike, this is not a good thing. We're past the point of Fed easiness being good for markets. If they do hike with the fed funds futures only pricing a 25 percent chance of it, I think you could have a big dislocation."
Boockvar said he expects stocks to sell off after the immediate pop. "I think you sell that rally. People are going to realize the Fed has no bullets," if it doesn't hike, he said. "If they don't raise rates and they're very dovish, I think the dollar is a sell on the news," he added.
George Goncalves, head of rates strategy at Nomura, said he does not expect the Fed to move yet but if it does, and it sounds extremely dovish, it may not hurt the markets or be disruptive. The two-year yield was at 0.70 percent late Friday, and the 10-year was at 2.19.
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"If they were to hike and they make it seem like it's only more of an operational thing and they are very dovish in how they communicate ... if they really go out of their way to make it a so-called dovish hike, I think the markets would take it in stride but there would be an adjustment mostly in the front end of the yield curve. Money markets would have to take a pause and recalibrate but the overall bond market would take it in stride," he said.
"If it's a dovish kind of hike and they're going to go slower that should be favorable for the five-year, 10-year part of the curve. The 30-year could start to get volatile because that's where inflation fears would show up the most."
Stocks in the past week closed higher, with the Dow gaining 2 percent to 16,433, for the best week since March 20. The S&P was up 2 percent to 1,961 in its best week since July 17.
Paulsen said he expects stocks to take another run at the August lows, even if there is an immediate bounce on the Fed this week.
"I think we're going to go back and challenge those old lows at some point, and I think we fail. My guess is (the S&P 500) breaks 1,800. We need to get to a lower valuation foundation, which we really haven't done yet," he said. "If it just goes right back up, we still have all the same challenges we had before. We've got to bring valuations down, and we need to scare people. I don't see fear."
September is a typically weak month for stocks, and the S&P 500 is now down 4.8 percent year to date. According to Jeff Hirsch, editor in chief of the Stock Trader's Almanac, the first half of September is usually better for the market than the back half. He said the coming week is the triple-witching expiration of futures and options, which can bring its own volatility. But historically, it is the week after September triple witching that is very weak.
"The week following has been down 21 of the last 25 years," he said.
8:30 a.m.: Retail sales
8:30 a.m.: Empire state survey
9:15 a.m.: Industrial production
10 a.m.: Business inventories
FOMC meeting begins
8:30 a.m.: CPI
10 a.m.: NAHB survey
4 p.m.: TIC data
Final day of FOMC meeting
8:30 a.m.: Initial claims
8:30 a.m.: Housing starts
8:30 a.m.: Current account
10 a.m.: Philadelphia Fed survey
2 p.m.: Fed statement
2:30 p.m.: Fed Chair Janet Yellen news briefing
10 a.m.: Leading indicators
1:30 p.m.: San Francisco Fed President John Williams on the economic outlook
3:30 p.m.: St. Louis Fed President James Bullard on the economy and monetary policy