After that, the market tends to succumb to exhaustion. The S&P 500 has historically then tripped into another meaningful decline within only two months. Five of the subsequent declines were pullbacks(declines of five to 10 percent) and six were corrections (10 to 20 percent).
"So this time around, it may be wise to fasten your safetybelt once we set a new high," Stovall says. "We may then be in for a bumpyride."
Stovall said, in a recent interview, that it may take several tries to even break above the 1565 closing high. "I think the market is getting a little tired, at the 1550 to 1565 level," he said. "I think most people acknowledge that the market has a hard time breaking through an important resistance level on its first attempt."
If the stock market does start to fall after hitting its highs, there are stocks that might hold up relatively well.
JPMorgan's chief U.S. equities strategist Tom Lee recently came up with 15 stocks that outperformed the S&P 500 in eight of the last 11 pullbacks since 2009. In other words, these are stocks that could be seen as relatively safe even in the anticipation of a stumble.
Those stocks? ConAgra, IBM, Disney, Genuine Parts Co, 3M,Fiserv, Paychex, PPG, Sysco, Sigma-Aldrich, Union Pacific, ,United Technologies Praxair, Loews, and DENTSPLY International.
These names boast great brands, solid management teams and they're easy to understand, Lee tells CNBC. "It's easy to justify why you would want to own them," he says. "IBM isn't going anywhere because the stock market might be about to sell off."
Lee turned near-term cautious several weeks ago, in response to an increase of bullishness among investors and his expectation of weakening economic data, due to higher taxes and gasoline prices.
(Read More: No 'Irrational Exuberance' in Stocks Now: Greenspan)