"We should get some indication of who approves of what Japan is doing and who is not bothered by the weak yen," said Gilmore. On a whole, Gilmore does not expect much news. "I don't think there's much headline risk attached to the G-20 in the next couple of days."
The latest U.S. jobless claims number is particularly important because it measures the same week that the government uses as the survey week for April payroll employment. Economists expect to see 350,000 claims, after last week's 346,000, a surprising 42,000 drop from the week before. The big differences were blamed on seasonality and the Easter holidays.
"Unless the number really moves significantly, I don't think it's going to tell us much about the payrolls number," said Joseph LaVorgna, chief U.S. economist at Deutsche Bank. LaVorgna expects the April jobs report, released May 3, to show 190,000 jobs were created, up from the 88,000 in March.
(Read More: Fed's Beige Book: Construction, Auto Sales Boost Economy)
Employment is the most important economic gauge for the markets, both because it speaks to the health of the economy and also because the Fed uses employment as a metric to determine how long it should ease. The Fed in recent weeks has sent ripples through financial markets, when some Fed officials began speaking about tapering the QE asset purchase program as early as the summer. The markets had expected it to begin to wind down later in the year.
But a series of weaker U.S. economic reports and some soothing comments from Fed Chairman Ben Bernanke and the other more dovish Fed members have outweighed the more hawkish comments.
So have fears about a global growth slowdown. One of the latest worries came from Europe Wednesday, where new car sales declined a steep 10.2 percent in March. That report was one factor in already gloomy markets. Commodities continued to sell off Wednesday, with copper plunging through a key technical level, and oil was down another 2 percent.
The Dow was off 138 points to 14,618, and the S&P was down 22 to 1552. U.S. stock futures were slightly higher in evening trading, but Asian markets followed through on the weakness in U.S. and European equities.
(Read More: Scary Pattern Could Be Forming on S&P 500 Chart)
What to Watch
On Thursday, CNBC's Steve Liesman interviews Richmond Fed President Jeffrey Lacker at 8 a.m. on "Squawk Box." Other Fed officials speaking Thursday include Minneapolis Fed President Narayana Kocherlakota, who speaks at 9 a.m. at the Ford Foundation, and Fed Gov. Sarah Bloom Raskin at 12:30 p.m., also at the Ford Foundation. Lacker speaks at 9:30 a.m. at the Richmond Fed's Credit Markets Symposium, and Fed Gov. Jeremy Stein speaks at the IMF conference on financial regulation.
(Read More: Copper Falls Below Key Level; Warning Signs Flash)
Besides the 8:30 a.m. ET claims data, there is the Philadelphia Fed survey and leading indicators, both at 10 a.m.
There are also dozens of earnings reports, including a big wave of tech names after the closing bell. Morgan Stanley, PepsiCo, Philip Morris, Verizon, United Healthcare, Nokia, Baxter, Peabody Energy, PPG, Freeport McMoran, Union Pacific, Sherwin Williams and AutoNation report before the opening bell. Google, IBM, and Microsoft report after the close, as do Advanced Micro Devices, Chipotle Mexican Grill, Intuitive Surgical, Capital One, and Celanese, E*Trade.
SeaWorld Entertainment IPO prices after the bell.