The ISM manufacturing survey is expected at 10 a.m. ET and is forecast to come in at 53.9, up from 53.1 in February. Auto sales, released by manufacturers, are expected to show a 15.8 million annualized selling rate, up from 15.3 million in February. There is also construction spending at 10 a.m. and Markit manufacturing PMI at 8:58 a.m.
"When it (ISM) went down from 56.5 to 51 in January, obviously people were shocked and initially people attributed it to the weather," said Stephen Stanley, chief economist at Pierpont Securities. "I think the readings late last year when it was consistently printing 56/57, I think those numbers were too high. I don't expect to get back to that level."
Markets are most sensitive to the monthly jobs report, expected Friday, but all data are key since the Fed is moving away from its quantitative easing, bond-buying program, based on its belief that the economy is improving.
Fed Chair Janet Yellen, who rattled markets earlier in March, gave stocks a boost Monday when she said the Fed would stay accommodative and provide extraordinary support for some time. Yellen's dovish tones countered a comment she made during her first press briefing that the Fed could raise rates within six months of ending its bond-buying program.
Read MoreYellen: Job market needs low rates 'for some time'
"I think there's a general disconnect between what the Fed thinks and what the market thinks," said Briggs. "The market has pushed up the timing of the first rate hike from August to May of 2015, and the Fed is clearly pushing back against that. If you get strong data, that divergence could widen, and if it's weak data, the market is more likely to listen to the Fed's dovish overtone."
As for Yellen's comments Monday, "It may be one of the most dovish things I've ever read. It's a campaign speech for low rates rather than a policy speech," he said.
Markets kick off the second quarter Tuesday, after the first quarter's mixed performance. The S&P 500 was up 1.3 percent, finishing at 1,872, while the Nasdaq was up 0.5 percent at 4198. The Dow, however, fell, losing 0.7 percent to 16,457. March was the worst month for the Nasdaq, off 2.5 percent, since October 2012, while the Dow and S&P were both high for the month.
"On face value, it looks fine, but there's a lot of frustration under the hood," said Scott Redler of T3Live.com, who trades the market's short-term technicals. He said he is watching the momentum names, which saw some buying Monday after days of selling. "Biotech held some gains for the first time." The iShares Nasdaq Biotech ETF was up 3 percent Monday.
"I think traders will be watching 1,875 on the S&P and then 1,883. If we close above those levels, we could go further," Redler said, adding new money for the quarter will be put to work sooner if the S&P can break that resistance zone.
Corporate buybacks have been a big driver for stocks, so a slowdown could be a concern for the market. Trim Tabs on Sunday said new buybacks in the first quarter of 2014 fell to their lowest level in five quarters. It said new stock buybacks totaled just $134.4 billion, well below the interim peak of $195.5 billion in the second quarter last year.
Moody's on Monday reported that U.S. nonfinancial companies held $1.64 trillion in cash at the end of 2013, up 12 percent from the year earlier. It said share buybacks increased 11 percent in 2013, while capital spending of $869 billion and dividends of $365 billion reached a seven-year high,
Read MoreChart of the day: Corporate cash kings get richer
Besides economic data Tuesday, stock traders will be watching Washington, where General Motors will be in the hot seat. GM CEO Mary Barra testifies before the House Energy and Commerce Committee about GM ignition troubles and why it took so long to deal with the issue and recall.
Read MoreGM recalls 1.5 million cars for steering defect
—By CNBC's Patti Domm. Follow her on Twitter