As the negotiations drag out, "the uncertainties of Brexit are many (and will likely) cause more volatility," Nuveen's chief equity strategist, Bob Doll, told CNBC.
But he doesn't expect another massive sell-off in stocks around a Brexit and said investors should focus more on U.S. corporate earnings since they are what fundamentally drive stock performance. He recommends being overweight U.S. stocks as "the most defensive market."
Many hope diminished headwinds of dollar strength and oil's plunge will help earnings. The U.S. dollar index is slightly lower year over year and crude prices are within $10 of the $55 level of last summer.
Large swings in oil prices drove much of the S&P's performance earlier this year. John Canally, chief economic strategist at LPL Financial, noted that oil has dominated the top-two or bottom-two performers for much of the year so far, but has recently had relatively more average performance.
That suggests "oil's influence on the market is waning a bit, as the fundamentals of oil (supply and demand are) now better reflected in the price," he said in an email.
However, the positive effects on U.S. growth likely won't be reflected until later in the year. The upcoming earnings season that officially kicks off in mid-July is still expected to show a fourth quarter of consecutive earnings decline. Investors are also watching for indications on how a Brexit potentially disrupts that outlook, or what impact China's slowdown has.
"Right now many analysts expect the second half of the year to show better revenue and earnings comparisons versus the first half," Nick Colas, chief market strategist at Convergex, said in an email. "A lot of that optimism was predicated on a weaker dollar. Now, the world has changed and a weaker dollar seems off the table. Will underlying fundamentals pick up the slack?"
The next employment report is due July 8, ahead of the Federal Reserve's meeting set for July 26 to 27. No news conference is scheduled until the Sept. 20 to 21 meeting.
"If we get another weak labor report for the U.S. that could set the tone for the third quarter," said Lee Ferridge, head of macro strategy, North America, at State Street Global Markets.
A weak May jobs report, and now the British vote to leave the EU will likely keep the Federal Reserve on hold past July and even September, maintaining an accommodative environment for stocks in the third quarter and keeping the dollar softer. But investors piled into the U.S. dollar as a safe haven trade after the Brexit shock and any uncertainty about global growth likely keeps the greenback elevated against major currencies. The dollar index has risen for the last two months for a quarterly gain of more than 1 percent.
Meanwhile, the U.S. presidential campaign will likely gain more focus in the third quarter as the November election nears.
"Both parties will host their nominating conventions and market participants will start looking for winners and losers in asset classes, sectors and individual stocks," Colas said. "Brexit was a warning sign that calling political outcomes is harder than it looks."
The Republican National Convention is scheduled for July 18 to 21 in Cleveland, while the Democratic National Convention is set for July 25 to 28 in Philadelphia.
Stocks have largely ignored the election so far, although the race between presumptive Republican presidential nominee Donald Trump and presumptive Democratic presidential nominee Hillary Clinton has been the talk of many trading desks.
"As the nonestablishment candidate, market volatility will be highly correlated with Mr. Trump's success in the polls this fall," David Lafferty, chief market strategist at Natixis Global Asset Management, said in an email. He did note the parties' battle for Congress did limit the impact of the presidential race on markets with about four months to the election.
History also shows third quarters of election years do tend to outperform.
For the S&P 500, the third quarter usually falls into the doldrums of "sell in May and go away" with a median gain of 1.86 percent since 1980, according to historical analysis using Kensho. But the analysis also showed that during U.S. presidential election years, the third quarter has a median return of 2.37 percent. The five occurrences should be taken with a grain of salt as positive trades were just slightly more than 50 percent.
China remains a wild card that could rock the third quarter. The country has quietly depreciated its currency against the U.S. dollar to multiyear lows amid market focus on a Brexit.
The third quarter wraps up with a G-20 leaders' summit scheduled for Sept. 4 to 5 in Hangzhou, China, the same city as Alibaba's headquarters.
"It's looking like it will be more form than substance. A surprise to the upside would be welcome," said Scott Kennedy of the Center for Strategic and International Studies. He also noted potential volatility from a negative reaction to The Hague's court ruling on the South China Sea dispute between the Philippines and China, due July 12.
Disclosure: CNBC's parent NBCUniversal is a minority investor in Kensho.