Economists expect the ADP report to show that 178,000 private sector payrolls were added in September, up slightly from 176,000 last month. The government's employment report for August showed that 169,000 nonfarm payrolls were created. For now, markets will have just the ADP number and other employment anecdotes to consider.
"(ADP is) what people will gravitate to, and they'll put a lot more stock in it," said Kevin Grady, president of Phoenix Futures and Options. "I don't think there's a direct correlation between the jobs number but I do think people will be trading off that number."
Deutsche Bank economists said they think the ADP survey is improving in terms of its predictive quality and the average miss between it and the government's private sector payrolls is 3,000 over the past year, compared with 29,000 in the prior 12 months.
The economists forecast 170,000 private sector jobs in the ADP report. They also forecast the government's report on nonfarm payrolls to show 170,000 jobs added in September, when it is finally released.
(Read more: 800,000 out of work as US government shuts down)
Diane Swonk, chief economist at Mesirow Financial, expects ADP at 175,000 private sector jobs for September; she also expects the government employment report to show the same when it is released. She said ADP also relies on government data. "It's accurate retroactively because they use the payroll data to adjust it," she said. "I like ADP because they break it down by manufacturing and construction but it doesn't always correlate on the seasonals."
Swonk said it's too early to see hiring for the holiday shopping season and she's concerned with increased headlines on layoffs. On Tuesday, Merck said it was laying off 8,500 workers. "We are seeing things like all the layoffs in mortgage origination across the banks. The retail hiring has been really mixed. Wal-Mart is hiring, and Amazon is hiring a little more than last year because they're hiring for warehouses," she said.
Tom Simons, money market economist at Jefferies, said the loss of fresh jobs data is particularly difficult because of the Fed. "Thank God they didn't taper. They showed some pretty good foresight and they cited the looming budget issues as a reason they wouldn't withdraw the purchases right now…I don't think anyone foresaw a long shutdown, but now it looks like it could be long," he said.
The Treasury has said the U.S. would hit the debt ceiling Oct. 17 if Congress does not act to raise it. "The only way we're going to get a resolution on both is from a combined negotiation," Simons said. "I don't see they're being enough time to get through the budget stuff between now and the debt ceiling debate, and I don't' see motivation in Washington to separate the two."
Now economists are trying to determine how much damage there will be to the economy from the government shutdown. Swonk said it now looks like the shutdown may stretch on longer than the few days initially expected. "It's about 0.5 percent of growth a week, and it starts to accumulate because you get collateral damage," she said. Roughly 800,000 government workers were put on unpaid leave, and it's unclear how many more could be added.
(Read more: US manufacturing activity highest since 2011)
She said the shutdown will stay the Fed's hand for the near future. Some economists expected the Fed to take action at its late October meeting, and more had expected it to wait until December after it held off tapering in September. "They can't do anything until this is resolved, and they have to wait to see how much damage there is. This clearly is one of the things they were concerned about," she said.
Deutsche Bank economists forecast that the shutdown would trim gross domestic product(GDP) growth by 0.1 percent initially but then intensify to 0.2 if the shutdown extends into a third or fourth week. They forecast that lost wages for the government workers furloughed Tuesday could be more than $150 million a day. Deutsche Bank chief U.S. economist Joseph LaVorgna said he had expected fourth quarter GDP growth of 3.5 percent but that could change based on the shutdown.
"I'm still optimistic," he said. "It's going to be temporary. Even if it were a few weeks, it's not enough by itself to derail the economy," he said. LaVorgna said manufacturing data is improving, including Tuesday's release of ISM data, which rose to a surprise 56.2, its strongest reading since April 2011. "It definitely looks better. The one piece that's been weak is employment, and unfortunately we're not getting that."
The stock market Tuesday closed higher, shrugging off the shutdown, after Monday's selloff. The Dow Tuesday rose 62 to 15,191, and the S&P 500 gained 13 to 1695. Stock futures were flattish in evening trading Tuesday.
Precious metals were pounded Tuesday, with gold falling 3 percent. The U.S. dollar was also weaker.
(Read more: Gold tumbles as investors watch Washington dysfunction)
The Treasury market for the most part was complacent, with yields moving slightly higher. But there was one corner of the market where the wrangling in Washington did have direct impact. There was weak demand for the Treasury's sale of $35 billion in 4-week bills. The bills were auctioned with a yield of 0.12 percent, up from 0.015 percent last week and zero the week before. The auction saw the weakest bidding for the maturity since 2009.
Simons said the auction was not a sign of stress but of traders looking at the duration as being the time when the U.S. would conceivably be heading for default if the debt ceiling is not addressed. "It is absurd…if there was risk of default it would be a much higher yield. It's not like this is indicative of some kind of stress for funding for Treasury. It's just that people like to play some investments and try to make trades based on these things," he said.
There are $20 billion in 7-day bills offered Wednesday, which should go smoothly, he said.
Simons expects the bond market to react more if the shutdown drags on. "It was an oscillating day in a little range. I think if we get close to the debt ceiling or if the shutdown lasts more than two weeks there will be a little bit of a rally," he said.
—By CNBC's Patti Domm. Follow here on Twitter