"You could have a blockbuster number on anything, and unless negotiations improve or they come to a deal, which isn't going to happen tomorrow, this is going to be an overhang," said Art Hogan, chief market strategist at Wunderlich Securities.
Markets were steadier Tuesday, after Monday's selloff. The S&P 500 ended Tuesday, up 5 at 2,063. But it ended up flat, or just 0.2 percent higher for the first half of the year, in the smallest move for the first two quarters since 1928.
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John Briggs, head of strategy at RBS, said bond traders will be reluctant to get short ahead of Greece's Sunday referendum on the bailout.
"Bigger picture, because there's a risk aversion, and you don't want to fight the tail risk that sometimes happens with Greece, investors are going to be reluctant to price in more of the Fed even if we have a good employment report," he said. "But if Greece clears up, then you would expect to see yields rise as we refocus on a good domestic economy."
Deutsche Bank chief U.S. economist Joseph LaVorgna said if the June report is weak on Thursday, the markets will continue to move expectations for the first Fed rate hike further into the future. According to RBS calculations, the market is placing odds of a September rate hike at 30 percent. It had been at 60 percent in early June.
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"Unless there's some breaking news between now and 8:30 Thursday, the Greece situation has negated the importance of employment," said LaVorgna. "If the number's really strong, I don't think people are going to care that much because Greece is going to be hanging over everything. It's like a free pass."
Besides ADP on Wednesday, there is the key ISM manufacturing survey; car sales and construction spending, all important.
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"The more important number is construction spending. Car sales are going to be good, but they're going to be weaker because last month was so strong," LaVorgna said. "If we get a decent construction number, people might be marking up their Q2 GDP number. People might start talking about construction being a tail wind to growth."
LaVorgna expects a 1 percent gain in construction spending. ISM is expected at 53 and it should show growth but it usually overshadows construction, he said.
"The nominal numbers for construction were up 14 percent over the last three months because of nonresidential structures which were up 24 percent," he said.
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