Despite months of urgent summits, repeated rescue plans and merciless budget cuts, European governments remain on the edge of a financial abyss, struggling to meet mountainous debts accumulated over four decades of living beyond their means.

The most immediate danger lies in Greece, where the government is effectively bankrupt, with debts amounting to an estimated 160 percent of the country’s gross domestic product. Negotiations with creditor banks, which have been asked to take a 50 percent loss, are proceeding fitfully in Athens. No one can predict the outcome, but European leaders assert they will not let them fail, and a coalition of creditors said Saturday that a deal might be reached in the week ahead.

Failure would be likely to put pressure on Greece to abandon the euro, the common currency used by 17 of the European Union’s 27 members. That, in turn, could touch off a cascade of financial turmoil, experts warn, endangering the E.U. and eventually crossing the Atlantic to undermine hopes for economic recovery in the United States.

Fellow European governments, meanwhile, warn that they will not pay out the next $170 billion installment on a separate E.U. rescue package for Greece unless the government legislates and puts into practice a new round of promised austerity measures. The tough cutbacks have been stalled for several months in the face of resistance, not only from an already-squeezed population, but also from the legislators and bureaucrats who are supposed to enact and enforce them.

European leaders, seeking to restore confidence in skeptical financial markets, announced after an all-night summit in December that they would negotiate a treaty binding governments to limit the perennial budget deficits that are the root of the crisis. After weeks of mid-level negotiations, a proposed treaty has been prepared for presentation at another extraordinary summit, scheduled for Monday in Brussels, an E.U. spokesman said.

That is a record time for the European community, where such negotiations usually move at a snail’s pace. But economists and officials point out that, in the latest drafts, the new treaty changes little from previous anti-debt commitments that over the years were simply ignored by European governments in need of extra financing.

One recent draft, for instance, contained a clause allowing E.U. governments to run deficits above the agreed cap “in periods of economic downturn,” setting the stage for a repetition of what happened to earlier no-deficit agreements. The European Central Bank, smelling a return to old ways, warned against any provision that would allow “easy circumvention” of the new rules.

In addition, the proposed treaty, despite its promise of Europe-wide deficit caps, would take at least several years to bring down government debts. As a result, it would have little effect on the immediate financial crisis, in which Greece is looking for a swift rescue and Italy, Spain and other countries face the prospect of paying back large bond issues coming due over the next few months.

“One could have just saved the big waste of time and energy it took to negotiate this international contract,” Luxembourg’s foreign minister, Jean Asselborn, said in an interview with the German newsmagazine Der Spiegel. “Most of what they want to regulate could easily have been done in the existing system.”

A European economist closely involved in E.U. affairs put it even more bluntly, under the cover of anonymity to avoid offending his contacts: “They just wanted a new treaty to make it look like they were doing something,” he said.

Ratifying new rules

It still is unclear how many countries will participate in the new rules, an E.U. official said. Britain from the beginning refused to hand over that much sovereignty. The Czech Republic and Sweden said they would have to check with their national legislatures; they have not yet announced the outcome. The other 24 countries signed on — some of them reluctantly, as a show of European solidarity.

Moreover, ratification could pose a problem in some countries. Ireland is weighing whether a referendum would be necessary under its constitution. In France, the Socialist candidate for presidential elections this spring, Francois Hollande, has said that, if elected, he would repudiate the agreement.

Daniel Gros, who heads the Center for European Policy Studies in Brussels, said focus on the treaty announcement in the pre-dawn hours of Dec. 9 eclipsed a much more important announcement the day before, from the European Central Bank in Frankfurt. The bank said it would loan money to European banks for three-year terms at 1 percent, an unprecedented deal that by the end of the month had pushed more than $640 billion into the cash-starved European banking system.

“That was the key,” Gros said. “That turned around the banking system.”

Recent bond issues by France, Italy and Spain drew investors at less-than-expected rates, suggesting that the markets have relaxed since the infusion. Most of the European Central Bank loans were not funneled back into purchases of government debt, however, but went to recapitalize the banks and enable them to pay their own debts while making loans to businesses, Gros noted.

The hope was that freeing up funds for the banks — making more loans possible and restoring confidence among lenders — would inject some movement into Europe’s stalled economies, which the International Monetary Fund expects to contract this year by an average of 0.5 percent.

“Buying some government bonds was a nice side effect but not really the point,” Gros said. “Now, European banks have assets. It is not that everything is nice, but the big credit crunch has not arrived. What the governments did was totally useless. It was beside the point.”

Hesitance in Germany

The real solution, Gros said, would be for the European Central Bank to show willingness to buy government bonds directly, becoming a lender of last resort. The French president, Nicolas Sarkozy, repeatedly has urged that course. But his main partner in E.U. affairs, Chancellor Angela Merkel of Germany, has steadfastly refused.

For her and the German financial establishment, including the Frankfurt-based central bank, the institution’s main mission is to manage the euro to prevent inflation, not to absorb debt caused by profligate government spending. Behind the reluctance lies a feeling that Germany, as the E.U.’s strongest economy, would end up contributing most of the money if the E.U. bank started steering funds into loans to financially unsteady nations such as Greece, Italy and Spain.

Similar fears have undermined efforts to bolster the European Financial Stability Facility, an emergency fund for heavily indebted E.U. countries that currently has about $320 billion in its vaults. The fund is to give way in July to a permanent fund that will be called the European Stability Mechanism and is supposed to be capitalized at $650 billion.

Since Germany is expected to put up the majority, Merkel has insisted that the leftover $320 billion can be folded into the European Stability Mechanism, for a total approaching a trillion dollars, only if the new treaty contains sufficiently binding deficit limits.

Her insistence on fiscal discipline, particularly in heavily indebted southern European nations sometimes called “the Club Med countries,” has provoked irritation in several capitals, including Paris. But since she holds the purse strings, the resentment rarely emerges publicly.

On a French television puppet show, however, she was recently portrayed as a schoolmarmish figure hectoring a child-size Sarkozy because he had blown his weekly allowance.