The fall over the fiscal cliff was far shorter than many had feared, prompting Wall Street to kick off 2013 with a 250-point buying binge.

But could this euphoric response turn out to be an overreaction to the upside?

After all, the short-term budget deal reached in the late hours of New Year’s Day sets the stage for another round of bruising battles over long-term deficit reduction, mandated “sequestration” spending cuts and the delicate matter of raising the debt ceiling to prevent an unthinkable default.

It’s easy to see how one or all of these debates could quickly engulf investor sentiment, more than wiping out Wednesday’s knee-jerk rally.

“I don’t want to throw a wet blanket on this feel-good rally. I don’t want to be that guy,” said Peter Kenny, managing director at Knight Capital Group (KCG). Still, he conceded, “there is a legislative battle in the offing that is going to make this look like a minor-league event.”

Back From the Brink                              

For now, investors are clearly focused on the positives of reaching a deal that allowed the U.S. to claw back from the recession-inducing cliff, for now.  

Including strong gains from Monday afternoon when the framework for a deal finally took shape, the Dow has rallied about 3.2% in just two days -- marking its strongest performance since November 2011.

“There was no real solution, more of a postponement but there is joy in being still alive,” Art Cashin,    UBS’s (UBS) director of floor operations at the New York Stock Exchange, wrote in a note to clients.

Ed Yardeni, president of investment advisory Yardeni Research, said the S&P 500 should soon make a new cyclical high and shatter all-time records later this year.

“If the stock market continues to rally, as I expect, even rich folks facing higher taxes will be happy to see their equity portfolios appreciate,” Yardeni wrote in a note.

Analysts at J.P. Morgan Chase (JPM) projected just a one percentage point reduction in 2013 gross domestic product growth from the fiscal cliff deal. That’s a huge improvement from forecasts of a four-point in GDP growth if the full impact of the cliff took effect.

Short-Lived Party?

Still, the failure to reach a more comprehensive agreement should limit the euphoria on Wall Street.

“Our clients are taking advantage today of a very obvious relief rally, but no one is thinking this is the start of a bull market,” said Laurence Wormald, head of research at SunGard’s APT, whose clients include some of the world’s largest pension, sovereign wealth and hedge funds. “Everyone understands we have debt ceiling and sequester reversal votes coming up and the politics are not much changed.”

A new analysis by APT suggests the relief rally will last no more than two or three days, adding a maximum of 5% to the S&P 500. Wednesday’s rally alone already drove the S&P 500 up almost 2%.

“We don’t expect it to go much further,” said Wormald.

The most immediate reason to be cautious about the fiscal-cliff deal is the headwind caused by the expiration of payroll tax holiday. That means most Americans will have an additional two percentage points taken out of their paychecks.

“That eats up a good part” of typical income growth and “should put a dent in discretionary consumer spending,” said Bruce McCain, who helps oversee more than $20 billion as chief investment strategist at KeyCorp.’s (KEY) Key Private Bank.

According to Deutsche Bank (DB), the expiration of the payroll tax holiday is worth about $110 billion in lost 2013 disposable income to U.S. households, subtracting about 0.75 percentage points of real GDP growth.

Likewise, McCain doesn’t see U.S. companies worried about the fiscal cliff becoming “a lot more aggressive about investing in their businesses” than they were before the deal was reached.

Debt Ceiling Debacle Part II?

Looking out just a few months, equity investors now have to worry about another pair of looming events that were left unsettled by this week’s compromise: mandated $90 billion of painful spending cuts and the $16.4 trillion debt ceiling.

The two issues may end up being tied together, further clouding the outlook.

Analysts at Barclays (BCS) warn that there is a “strong possibility” policymakers in March “follow the same game plan” of going to the “brink before coming to an incomplete solution.”

Technically the U.S. hit the debt ceiling last week but the Treasury Department will employ accounting tricks to avoid a default for the next few months.

Investors need only to remember the turbulent days of the summer of 2011 to see how jittery the markets can become over the debt ceiling. Brinksmanship on this matter nearly led to an unprecedented U.S. default on its debt, and the removal of the country’s AAA credit rating from Standard & Poor’s for the first time ever.

Poisonous Atmosphere

The risk now is the debt ceiling talks could lead to steep market declines, another downgrade by a ratings company or even a once-unthinkable default that could spook the global financial system.

This debate is potentially more delicate than the fiscal cliff one because Congress doesn’t have the option to undo a default, as it did with the fiscal cliff.

Given the stalemate of recent weeks, the tone in Washington is also decidedly more negative compared with the last time the debt ceiling was debated.

“This was not an amicable compromise. Both sides tried to bludgeon the other,” said McCain. “The rancor suggests the continued need for discussion and compromise is going to be even more difficult than it was in this experience. I’ve seen union negotiations that are more amicable than what we had here.”

All of this helps explain why some market watchers are preaching caution in the medium term as enthusiasm for this relief rally is likely to fade.

“The downside risks have not gone away. They’ve been pushed away for a couple of months,” said Wormald.

Follow Matt Egan on Twitter @MattMEgan5