"I wouldn't expect a big reaction to a surprise on the downside," said Ed Keon, chief investment strategist at QMA. "There's still enough information showing that inflationary pressures are rising. It's much more likely to have a negative reaction if there's an upward surprise. ... If it came out up 0.4 percent, given everything else that's going on, I think you'd see a negative reaction."

Economists expect Thursday's CPI data to reveal a 0.2 percent increase in both headline CPI and core CPI, excluding energy and food, according to Thomson Reuters.

Consumer price inflation data could temporarily take market focus away from trade worries, particularly if it surprises to the upside like Wednesday's producer prices.

Traders have been watching inflation data closely for any signs of a pickup, especially since wages are not showing much sign of improvement. A much higher pace of inflation could speed up Fed rate hikes. So far, inflation has edged above the Fed's 2 percent target but not gone much further. CPI core is expected to show an annual pace of 2.3 percent in June.

Stephen Stanley, chief economist at Amherst Pierpont points out that the Fed's preferred inflation metric, the core PCE deflator, finally reached the Fed's 2 percent target in May, for the first time in six years. He added that the Fed is no longer worried about inflation being too low, just whether it can sustain current levels.

“With growth well above trend and the unemployment rate well beyond estimates of full employment, we should not be surprised that there are increasing reports of price pressures including in the trucking industry, where freight costs are said to be exploding. I have long anticipated that inflation would likely continue to accelerate after finally reaching 2 percent, a scenario that neither the FOMC nor the bond markets seem prepared for,” he wrote.

"A 0.2 percent monthly gain for the CPI in June would likely push the year-over-year advance up to 2.9 percent for the first time in over six years, and I would not rule out a move to 3.0 percent," Stanley wrote in a note. But he adds that he would expect the pace to peak in June or July for 2018. He said June food prices likely increased but gasoline prices were probably steady.

Producer price inflation rose 3.4 percent in June, year over year, its biggest increase in 6½ years.

Keon said stocks held up well Wednesday in the face of new trade headlines, with the U.S. threatening tariffs on $200 billion in Chinese goods. "It's an interesting day in the sense we clearly had some negative news on the trade front," he said. "Not a huge reaction."

The closed at 2,774 down 19 on Wednesday.

"Holding between 2,755 to 2,765 will show some commitment to the recent quick, strong move we've seen in the past week," said Scott Redler, partner with T3Live.com. "If that were to hold, we could finally take out 2,800. The next headline everyone is waiting to see is what does Beijing do. Do they talk or is it tit-for-tat? Tit-for-tat makes for choppy trading."

CPI data will be released at 8:30 a.m. ET, as will initial claims data.