Treasury yields moved to lows after ISM manufacturing data unexpectedly slipped to 51.5 from 52.5, and new orders and the employment component were both lower. The 10-year bond was yielding 1.86 percent.
Stocks were down sharply but pared some of their losses by midday. The Dow had been down nearly 200 points, and the S&P 500 was down 13 points at 2,054.
A selloff on April Fools' Day is relatively unusual. In the last 10 years, there have only been two other instances—in 2013 and 2005, according to CNBC's analytic's partner Kensho.
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The ADP report also makes it likely economists will pare back expectations for Friday's government employment report, now expected at 245,000 new jobs. According to Thomson Reuters, the unemployment rate is also expected to remain unchanged at 5.5 percent.
"On the margin, this is going to moderate people's expectations for Friday. The lowest (ISM jobs) component since May 2013, and the lackluster ADP report has taken some of the more ambitious bias away from Friday's number," said Ian Lyngen, senior Treasury strategist at CRT Capital.
Economists have been expecting a spring back in the second quarter though the first quarter forecasts could continue to look even weaker. Thursday's trade data could have economists reducing growth forecasts even further as exports are likely to have been pinched by the higher dollar. According to the CNBC/Moody's Analytics rapid survey, economists expect growth of 1.3 percent for the first quarter.
Economists have been writing off the first quarter as a weak period, impacted by winter weather. The dollar impact, however, could be a factor that creeps into the second quarter, and the extent of its influence is a concern.
Read MoreWeak ADP sets up dovish bets for jobs report
Zane Brown, fixed income strategist at Lord Abbett, said the ADP report showed a clear weakening due to the dollar, and that could show up in Friday's report for March employment. Brown said ADP added only 5,000 goods producing jobs compared with a recent average of more than 30,000.
"It also corresponds with a pretty significant drop in jobs at large companies," he said, noting they added 19,000 jobs compared with more than 50,000 in recent months.
"Really, the large companies that are producing goods, it really suggests that the dollar is influencing their willingness to hire as well as earnings," he said. "If this really is a function of manufacturing at large companies and it really is a function of a dollar impact, then it could affect the Friday number as well."
The markets have been fixated on Friday's new nonfarm payroll jobs number, setting it up as an important clue for timing on the Fed's first interest rate hike. Strategists said if the number were much higher than expected, it could signal that the Fed would consider a rate hike as early as June. The market now expects a rate hike in September or later, and the ADP report reinforced that view.
Very weak data could mean the Fed will take its time to move on rates, making September forecasts too aggressive.
Boockvar said he thinks the market is coming to terms with the expectations that earnings could decline for the first time in six years, just as he Fed moves toward interest rate hikes. Bad news may once more be viewed as negative, instead of as a reason for the Fed to be easy.
"To me, buying stocks because the Fed may not raise, is running out of gas. We had three major boosts to the market—QE, zero rates and the strong earnings story," he said.