WASHINGTON – Onward to the next fiscal crisis. Actually, several of them, potentially. The New Year’s Day deal averting the so-called fiscal cliff lays the groundwork for more combustible struggles in Washington over taxes, spending and debt in the next few months.

President Obama’s victory on taxes this week was the second, grudging round of piecemeal successes in as many years in chipping away at the nation’s mountainous deficits. Despite the length and intensity of the debate, the deal to raise the top income tax rate on families earning over $450,000 a year — about 1 percent of households — and including only $12 billion in spending cuts turned out to be a relatively easy vote for many. This was particularly so because the alternative was to raise taxes on everyone.

But in banking $620 billion in higher taxes over the coming decade from wealthier earners, Obama and his Republican rivals have barely touched deficits still expected to be in the $650 billion range in the final year of his second term. And those back-of-the-envelope calculations assume policymakers can find more than $1 trillion over 10 years to replace automatic across-the-board spending cuts known as a sequester.

“They didn’t do any of the tough stuff,” said Erskine Bowles, chairman of Obama’s 2010 deficit commission. “We’ve taken two steps now, but those two steps combined aren’t enough to put our fiscal house in order.”

Resolving the tax debate did buoy stock markets Wednesday. The Dow Jones industrial average finished up 308.41 points to 13,412.55, and the S&P 500 closed up 36.23 points to 1,462.42. The tech-heavy Nasdaq ended up 92.75 points to 3,112.26.

Yet shortly after the markets closed, the rating agency Standard & Poor’s warned that Washington didn’t accomplish enough to remove the threat of further downgrades on the creditworthiness of U.S. government debt, according to McClatchy Newspapers.

“While congressional compromise designed to avoid the ‘fiscal cliff’ may support the still-fragile U.S. economic rebound, the compromise doesn’t affect our view of the country’s credit outlook,” the agency said. “We believe yesterday’s agreement does little to place the U.S.’s medium-term public finances on a more sustainable footing.”

Similarly, Moody’s Investors Service said Wednesday that the deal amounted to just a “further step” in clarifying the deficit and debt trajectory.

“It does not, however, provide a basis for a meaningful improvement in the government’s debt ratios over the medium term,” Moody’s warned, making it clear that the United States remained on its negative watch list, where it’s been since September.

If Moody’s joins Standard & Poor’s in downgrading U.S. bond ratings, borrowing costs for the already heavily indebted government might rise sharply. And if more than one rating agency takes away the AAA rating on U.S. debt, big pension funds and endowments that are required to hold only the safest of government bonds would have to shed their U.S. government bonds, McClatchy reported.

In 2011, the government adopted tighter caps on day-to-day operating budgets of the Pentagon and other Cabinet agencies to save $1.1 trillion over 10 years.

The measure passed Tuesday prevents middle-class taxes from going up while raising rates on higher incomes. It also blocks severe across-the-board spending cuts for two months, extends unemployment benefits for the long-term jobless for a year, stops a 27 percent cut in Medicare fees paid to doctors and prevents a possible doubling of milk prices.

The alternative was going over the cliff, an economy-bruising, half-trillion-dollar combination of sweeping tax increases and spending cuts. Despite the deal, the government partially went over the brink anyway with the expiration of a two-year cut in Social Security payroll taxes of 2 percentage points.

Action inside a dysfunctional Washington now only comes with binding deadlines. So, naturally, this week’s hard-fought bargain sets up another crisis in two months, when painful across-the-board spending cuts to the Pentagon and domestic programs are set to kick in and the government runs out of the ability to juggle its $16.4 trillion debt without having to borrow more money.

Unless Congress increases or allows Obama to increase that borrowing cap, the government risks a first-ever default on U.S. obligations. Republicans will use this as an opportunity to leverage more spending cuts from Obama, just like they did in the summer of 2011.

House Speaker John Boehner, R-Ohio, vows that any increase in the debt limit — which needs to be enacted by Congress by the end of February or sometime in March — must be accompanied by an equal amount in cuts to federal spending. That puts him on yet another collision course with Obama, who has vowed anew that he won’t let haggling over spending cuts complicate the debate over the debt limit.

The cliff compromise represented the first time since 1990 that Republicans condoned a tax increase. That has whipped up a fury among tea party conservatives and increased the pressure on Boehner to adopt a hard line in coming confrontations over the borrowing cap and the spending cuts that won only a two-month reprieve in this week’s deal.

The upshot? More scorched-earth politics on the budget will probably dominate the initial few months of Obama’s second term, when the president would prefer to focus on legacy accomplishments like fixing the immigration problem and implementing his overhaul of health care.

The relationship between Boehner and Obama has never been especially close, and seemed to have suffered a setback last month after the speaker withdrew from negotiations on a broader deficit deal. The two get along personally, but politically, a series of collapsed negotiations has bred mistrust. The White House has the view that Boehner cannot deliver, while the speaker is frustrated that matters brought up in his talks with the president are not followed through by White House staff.

And on the debt limit, Boehner and Obama at this point are simply talking past each other.

“While I will negotiate over many things, I will not have another debate with this Congress over whether or not they should pay the bills that they’ve already racked up through the laws that they passed,” Obama said after the fiscal deal was approved Tuesday.

Said Boehner spokesman Michael Steel: “The speaker’s position is clear. Any increase in the debt limit must be matched by spending cuts or reforms that exceed the increase.”