"I think he would wait for the finance ministers to speak. I don't think Draghi would say anything on his own about Greece," said Chris Rupkey, chief financial economist at Bank of Tokyo-Mitsubishi.
Traders are already looking ahead to Friday's nonfarm payrolls, expected at 225,000, so ADP's May report is an important warm up to the government data. ADP is expected to announce 200,000 jobs at 8:15 a.m. ET, up from 169,000 last month, according to Thomson Reuters. The government's report of 223,000 April nonfarm payrolls was well above the ADP number.
"ADP could be big. We've been reacting to it. If it's a 150,000 number, or something like that, if it's bad, bond yields could come down here. But the primary driver is what's going on in Europe and European yields," said Rupkey.
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The ISM nonmanufacturing survey is reported Wednesday, and the market is also focused on the employment component of that number.
"We need these anecdotes from ADP and ISM, all the things that will come in over the course of the next 48 hours before we start to hear updated, nonpublished estimates" of Friday's job number, said Ian Lyngen, senior Treasury strategist at CRT Capital.
Each month, traders speculate about whether the jobs number will be better or worse than expected, and some traders reported hearing speculation the number would be weaker than expected. But the real buzz will begin after the ADP report.
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Art Cashin, director of floor operations for UBS at the NYSE, said the key thing for markets will be Draghi. "ADP will be watched but I don't think the markets have fully embraced it yet," said Cashin.
Rupkey said the export number in the trade report will also be key. "We get one of (Fed Chair) Janet Yellen's risks out there ... exports. Exports got killed early in the year here," said Rupkey. "Partially we did have the West Coast dock strike. We had weather. ... If the Fed's concerned about weak data, the weakest of the weak data has been exports."
The export number in the first quarter was a drag on GDP, which contracted 0.7 percent.
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"Any big rise would be important if it were up 4 or 5 or 6 percent," said Rupkey. "It came down double digits. If it strikes back in the opposite direction by a significant amount that might be an interesting story. One more headwind that is fading."
Lyngen said besides Europe, rates also rose on Tuesday's better ISM manufacturing data and on the lack of liquidity in the bond market. "There has been a reduction in the willingness to take risk ahead of these big numbers. Just generally speaking, no one is willing to stand in front of these moves," he said.
Rupkey said nonfarm payrolls could pack a surprise that might impact the Fed's thinking on rate hikes. "The money number is going to be the unemployment rate. Yellen drew a line in the sand about 5 percent being full employment. I think the expectations are for unchanged, but there's a chance it would fall more than expected. It could go to 5.3 percent," he said. The consensus is for an unemployment rate of 5.4 percent.
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