Read MoreBuy stocks, S&P headed above 2,000: Ed Yardeni
"Typically in any weather-related disruption, 25 to 35 percent of the economic activity is lost, but the majority of it is just deferred," Kleintop said. "The pent-up demand should boost second-quarter results."
As things stand for the April-to-June period, analysts are expecting S&P 500 earnings to jump 8.3 percent, according to S&P Capital IQ. Subsequent quarters call for gains of 9.4 percent and 11.1 percent, for a full-year gain of 7 percent.
The market is hanging its hat on several factors for the expected rapid profit gains, with Kleintop expecting CEOs to raise future expectations when presenting their first-quarter reports.
"Positive forward guidance from corporate leaders may boost confidence in future earnings growth and help to lift stocks in the coming weeks," he said.
The jury's still out, though, on corporate optimism.
Read MoreHere's the one trend to watch in earnings season
Of the 110 companies that have released forward guidance, 75 have been negative, 33 positive and two in-line, producing a negative-to-positive ratio of 2.3 to 1, which is only a shade lower than the historical average of 2.4 to 1, according to S&P Capital IQ.
The earnings picture is critical considering that the market's rise of 180 percent since the March 2009 low had been virtually 1-to-1 with the earnings gain, but last year's 29 percent market gain distorted that relationship.
"The increase in the price-to-earnings ratio over the past year—with stock prices rising faster than corporate earnings—has been a focus of investors lately." Kleintop said. "Worries among market participants that this type of growth is unsustainable have led to sharp declines among some 'bubbly' stocks in certain industries."
The main question, then, is whether the economy is strong enough to support a substantially improved earnings picture.
Fairly strong signs have abounded lately, with March retail sales topping expectations, new weekly jobless claims threatening to dip below 300,000, and manufacturing indexes also improving.
Read MoreIs this a bubble market? Here's one way to tell
Tom Porcelli, chief U.S. economist at RBC Capital Markets, said there are plenty of reasons to believe the economy is strong enough to support better earnings and stock market gains. He points out that even with a below-trend 2.5 percent gain in gross domestic product in 2014, that still adds $400 billion to economic output.
"Think about the equity market and what GDP is going to advance by," he said. "When you think about the macro overlay, it's supportive of a fairly constructive view on the equity market."
For the year, the S&P 500 is up less than 1 percent. The bond market, meanwhile, is indicating tepid growth as well, with the 10-year Treasury note yielding just 2.72 percent even with a big jump in late-week trading.
Federal Reserve officials, though, reported seeing signs of stronger activity with the inclement weather receding. This week's Beige Book report offered a more positive tone than any other this year. The Fed itself has been a major cog in the stock market's growth as the central bank has expanded its balance sheet to $4.2 trillion through its monthly bond-buying program, currently at $55 billion.
Read MoreJobs market bounces back as weather effects wane
"That was one solid report," David Rosenberg, strategist and chief economist at Gluskin Sheff, said in his daily letter Thursday. "No matter the economic indicator, we are building some serious momentum into Q2, the question is just how much."'
Known more for his bearish observations, Rosenberg outlined the economy's multiple headwinds: "Income inequality. Credit constraints. A soft tone to the global economy overall. Long-term joblessness. Student debts. Aging demographics. Political sclerosis. Ukraine uncertainties."
He's shifted his tone, though, and believes the outlook is positive.
"While these pose limits on the extent of the growth we are seeing and will see, they are not going to prevent the economy from embarking on a visible improving trend of the next several quarters," he said. "They are hurdles, but I have never found structural impediments as being sources of reversal—it you are bearish on the economy, then be prepared to talk about the sort of negative shock you see coming and be ready to explain why this formulates your base-case scenario."