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The Fed's preferred inflation measure is the PCE Deflator, and that is running at about 1.6 percent, below the Fed's target of 2 percent inflation. But because core CPI has been running above 2 percent, traders have been watching it closely as higher inflation could cause the Fed to raise rates sooner.
CPI is released at 8:30 a.m. EDT, as are housing starts and building permits, while industrial production and capacity utilization are at 9:15 a.m. EDT.
Besides inflation, traders will focus on energy prices, which rallied more than 3 percent Monday. West Texas Intermediate futures rose to $47.72, and that helped lift energy stocks. The stock market also got a lift from a rally in Apple, after Berkshire Hathaway revealed that it owned a stake in the company.
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The S&P 500 rose 20 points to 2,066, a gain of nearly 1 percent.
Late in the day, there was some Fed-related chatter about an announcement that Fed Chair Janet Yellen would speak on June 6, just before the blackout period for the June Fed meeting.
"I look for nothing new on the rate front (at the June meeting). If they are going to pull the trigger in September, they're going to look to set the market up for that by talking hawkishly," said Mark Luschini, chief investment strategist at Janney Montgomery.
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He said he did not expect Yellen to tip her hand about the June meeting on June 6, but there was speculation Yellen may try to firm up a message for markets ahead of the June meeting.
Besides economic news, there are a few earnings reports Tuesday including Home Depot, TJX and Red Robin Gourmet. Home Depot and off-price chain TJX will be the latest to report after last week's string of disappointing chain store earnings and sales commentaries.
Home Depot reported earnings per share of $1.44, eight cents above estimates. The retailer raised its full year profit and same store sales forecasts.
"TJX I think has been somewhat immune from some of the retail malaise we've seen in some of the big box retailers. Home Depot addresses a whole different market that's been holding up pretty decently," said Luschini.
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There are also several Fed speakers including San Francisco Fed President John Williams and Atlanta Fed President Dennis Lockhart, who appear on a panel at 12:25 p.m. Dallas Fed President Rob Kaplan speaks at 1:15 p.m. EDT at a community forum.