There are also geopolitical threats, such as tension in the Middle East and how the U.S. will respond to the May 12 deadline to extend Iran's nuclear agreement. Talks are also being planned between President Donald Trump and North Korean leader Kim Jong Un on ending the North Korean nuclear program. Domestically, midterm elections are also a threat to the market, with concerns mounting that Republicans could lose their majority in Congress.
"I think May is an important month. We've been trading in a range of 2,600 to 2,800," said Parker. "We're about halfway through, so it's important psychologically to end the month closer to the top of the range than the bottom of the range."
Parker said he expects a recovery in market-leading technology, and he does not see inflation becoming a big problem for the market.
The economy also has more upside, which is one reason the Fed can continue to raise interest rates. It meets this week but is not expected to take any action until its next meeting in June.
"We don't think fiscal stimulus is really making its way into the economy until the end of this quarter or third quarter," Parker said.
The S&P 500 is flattish year-to-date after a wild ride higher at the beginning of the year, to correction lows more than once, with a lot of volatility in between.
"I think May could be a recovery month from what we have had recently," said Sam Stovall, chief investment strategist at CFRA.
While the S&P 500's total return in the May-through-October period has averaged just 1.2 percent in the past 20 years, it was higher 70 percent of the time. During the November-to-April period, the S&P was up 85 percent of the time, averaging a 6.2 percent total return.
Ryan Detrick, senior market strategist at LPL Financial, notes that midterm election years have on average lower returns in the May-to-October period than other years. But he also wrote that the April-to-November period in those years sees above-average returns.
Parker said important trade developments could come in May, with the Trump administration's talks in China this week and the decision whether to implement proposed tariffs. There is also the potential for an announcement soon on the renegotiation of the North American Free Trade Agreement.
"It is key for the rest of the year that we do have a May that's reasonably constructive, or positive," Parker said.
"It's better to rotate than retreat," Stovall said. Stovall said the three best-performing sectors on average in mid-term election years for the May to October period have been staples, health care and real estate.
Jack Ablin, CIO of Cresset Wealth, said investors may be shifting to small- and mid-cap stocks because they are less impacted by tariffs and trade issues, and they benefit from the tax bill.
"I worry about tariffs, and they'll likely have a negative effect, but once investors shift through the winners and losers they'll find small- and mid-cap stocks are somewhat insulated from that risk," he said.
Ablin said investors may also have found earnings season as a good time to take profits in technology names, and that could have added to pressure on those stocks even when earnings were solid.
"There's a lot of worry about tech. It's come through the earnings season as a relative in line performer. The tech rotation we did call for in mid-March has largely played through," said Parker, adding it was a stronger decline than he expected. "We were expecting it to lag amid a broader market recovery. ... What we got [was] a catch up in energy and others and a catch down in tech. That was not what we were expecting."
Parker said the net mix for technology has been positive for earnings and upgrades. "We have a few more reports. As we move out of this reporting season, the outlook for the sector is very strong," he said.
For the month of April, the S&P technology sector is up just 0.4 percent, compared with the 9.9 percent gain in energy, or the 2.6 percent gain in consumer discretionary names.
"We're obviously looking for upside to April for the rest of the year," said Jill Carey Hall, equity strategist at Bank of America Merrill Lynch. Hall said she expects the S&P to reach 3,000. She did note, however, that May is the third-worst month of the year, with a performance that averages out to be just about flat.
"The key things we are looking for in the market are growth, valuation and sentiment, and in our view all three of those are still supportive," she said. "Earnings growth has been very strong."