That could further pressure sales of U.S. companies with heavy international exposure because it makes U.S. goods more expensive overseas.

"If we have a similar movement to last year, then we're going to have roughly a $28-billion hit to corporate America," said Wolfgang Koester, chief executive of currency risk consulting firm FireApps. He said he expects the dollar to shave 3 to 4 cents from first-quarter earnings of U.S. companies with foreign exposure.

The Public Could Elect A Fringe Candidate

Stocks historically do well in a presidential election year, with the S&P gaining in 13 of the 16 presidential election years since 1950, regardless of which party won, according to the Stock Trader's Almanac.

But strategists wonder if 2016 might be one of the exceptions to the trend, with outliers like Donald Trump and Bernie Sanders running this year.

"The more extreme the candidate, the less well-received the candidate typically is by the stock market," said Kristina Hooper, U.S. investment strategist at Allianz Global Investors. She said she expected election activity throughout the year to contribute to market volatility.

The Fed Could Get Aggressive

The stock market rallied on Dec. 16 when the U.S. Federal Reserve announced its first rate hike along with strong hints that it would move slowly on future increases.

But if the central bank continues to raise rates without seeing higher inflation or an earnings pick-up, that could dent stocks. "Rate hikes should be a consistent worry," said Tim Ghriskey, chief investment officer of Solaris Group in Bedford Hills, New York.

As rates rise, stocks could become less attractive compared with other asset classes like bonds.