"We're going to refocus back on earnings season, and I think so far the numbers have been a little disappointing. I think perhaps we're going to stand a chance to have some retreat from this deal rally we've had," said Mark Luschini, chief investment strategist at Janney Montgomery.
Earnings news has been mixed with a few high profile misses, like IBM's report on Wednesday afternoon. IBM shares tanked nearly six percent in the after-hours session after it reported weaker-than-expected revenues. While still early in the reporting season, analysts note the pace of companies announcing better-than-expected earnings this quarter is slower than average.
Over the past four quarters, an average 66 percent of all S&P 500 companies beat earnings estimates. As of Wednesday morning, 57 percent of the S&P 500 companies had reported better-than-expected earnings, and 55 percent had beat revenue forecasts, according to Thomson Reuters.
(Read more: Wall Street not listening to Washington anymore)
Among companies due to report Thursday morning, Goldman Sachs will make its first report as a member of the Dow. Ahead of the opening bell, earnings are also expected from Philip Morris, Roche Holdings, Taiwan Semiconductor, UnitedHealth, Verizon, Union Pacific, Blackstone, Baxter, Peabody Energy, PPG Industries, Fifth Third, Alliance Data, Baxter, Sonoco Products, Winnebago and Huntington Bancshares.
Google, Chipotle, Las Vegas Sands, Stryker, Capital One and Advanced Micro will report after the closing bell Thursday.
The 16-day government shutdown has also left the markets starved for economic data, as many key reports that are released by government agencies were not released. Traders expect the September jobs report to be released about three business days after the government reopens, and the rest of the data, including inflation and retail sales, are expected to be released in sequence as numbers become available.
Weekly jobless claims, the only economic report the government has released, are expected at 8:30 a.m. ET Thursday. Economists expect 330,000 claims after last week's report showed a spike to 374,000. The Philadelphia Fed survey is also expected at 10 a.m. The Fed is self-funded so it has been issuing reports, like Wednesday's beige book on the economy.
"We're going to see heightened volatility around data releases because we've been in withdrawal. We were just following the politics, and now we're going back to following the fundamentals," said George Goncalves, Treasury strategist at Nomura Americas.
The fundamentals are also important to markets because they are followed by the Fed and help guide its decision on whether to slow down its quantitative easing purchases. Market participants increasingly expect the Fed to put off slowing its bond purchases until next year.
(Read more: Reid: Deal reached to end shut down, raise debt ceiling)
Some analysts expect that delay to be supportive for the stock market, which had been braced for a tapering announcement in September and was surprised when the Fed kept the status quo. Now with Fed Vice Chair Janet Yellen expected to take the helm of the Fed in January after Fed Chairman Ben Bernanke's term expires, the markets are expecting Fed policy to remain dovish.
"We don't have tapering, and we have the 'Yellen put,'" said Luschini. "In the great baton handoff between Bernanke and Janet Yellen, if anything the (current) pace of dovishness will be handed to her and could even accelerate."
Luschini said he expects the stock market to continue to do well, even with the 20 percent year-to-date gain in the S&P 500, but its immediate reaction to the Congressional compromise may be to pull back. The Dow has regained about 650 points in the past week, and the S&P is just eight points away from its all-time high.
But Tobias Levkovich, chief equity strategist at Citigroup, said the fact that Congress pushed off its deadlines on the spending resolution and debt ceiling to early next year raises more uncertainty, just as the Fed created uncertainty.
Fed officials' comments on possible tapering had fanned speculation that the Fed could announce a slowdown in purchases in September, or at least by December. Now that has changed and some, like Goncalves, expect the Fed to announce its first tapering in March.
Levkovich said in a note that "the twin decisions of a taper timing push out and the discord in Washington being swept under the run until January and February roll in could keep P/E multiples more compressed as equity risk premiums stay elevated," he wrote. "Investors typically do not like uncertainty and it is hard to determine how these recent almost non-decisions can be seen as reinvigorating confidence aside from some relief that an imminent likely disaster has been avoided."
(Read more: Relax! US won't run out of money Thursday)
Like others, he also points out that earnings estimates are too high for 2014.
"You've got an earnings season to get through with guidance, and that guidance has been affected by what's going on in Washington," said Art Hogan of Lazard Capital Markets.
Goncalves said the bond market was sending several signals Wednesday, including the anticipated delay in Fed tapering. But the market is also responding to slower-than-expected economic growth, and the lack of a second half bounce, which had been expected by many economists. Some economists had expected a roughly 0.2 to 0.3 percent hit to growth per week from the government shut down.
"On the darker side, maybe the bond market is anticipating weakness in this quarter and into 2014," he said.
He also said investors were not buying as many Treasurys as they normally would because of the debt ceiling risk. "People were kind of leaning a little short on their bench marks," he said. "There were a lot of people scared off by higher rates this year and rates (on the 10-year) going above 3 percent."
Goncalves said he expects to see the 10-year yield go back to the 2.50 percent level. "We dodged the bullet and there's a lot of cash on the sidelines, and it's going to benefit many asset classes. That's why stocks and bonds went up at the same time" Wednesday, Goncalves said.
(Read more: Prospect of deal eases pressure on short-term Treasury market)
There are several Fed speakers on the calendar Thursday. Dallas Fed President Richard Fisher will speak on monetary policy at 8 a.m. ET in New York. Fisher, an outspoken critic of quantitative easing, surprised markets this week when he said it makes sense for the Fed to take no action to curb bond buying at the October meeting because of the uncertainty caused by Washington.
Other speakers include Chicago Fed President Charles Evans, who will speak about the economy and monetary policy at 12:45 p.m., and Kansas City Fed President Esther George, who speak about the economy at 1:45 p.m.
—By CNBC's Patti Domm. Follow here on Twitter