Economists are increasingly questioning the relevance of the eurozone rescue fund as pressure builds on the European Central Bank (ECB) to lead a lasting and massive debt crisis response. The European Financial Stability Facility (EFSF), which uses 440 billion euros of government guarantees to borrow on markets for subsequent lending to bailed-out Greece, Ireland and Portugal, "has no credibility" with traders, said Belgian economics professor Paul De Grauwe. The fund, worth $595 billion at current exchange rates, was born out of the first phase of the Greek debt crisis 18 months ago but has constantly appeared behind the curve as financial market contagion sucks in country after country. Eurozone leaders decided at a summit late last month to "leverage" its lending capacity up to a trillion euros just as Italy's 1.9-trillion-euro debt mountain pushed it to the top of investor concerns. A new "technocratic" government has taken power in Rome, with its public finances put under EU-IMF surveillance while France -- the second-largest eurozone economy -- is the latest to see its borrowing costs under pressure. That means a timeframe announced by Luxembourg Prime Minister Jean-Claude Juncker for an upgraded EFSF to be partly operational in December, and fully ramped up in February, is looking increasingly irrelevant, the economists say. Britain, France and the United States have each urged Germany to allow the ECB to emulate the Federal Reserve or the Bank of England by funding governments and pumping liquidity into the eurozone, in effect printing new money in an effort to get the economy moving again. "The rescue fund, to begin with, will not have sufficient resources, even with a trillion euros," said De Grauwe, who lectures at Belgium's Louvain university. "Italy has almost two trillion in debts and soon we might be talking about Spain and France," he said. Yet the newly souped-up EFSF "can't even get out of the (starting) blocks," with markets already adding premiums to the fund's own borrowings. So ideas are multiplying on how to change the fund to make it live up to its objectives. Credit Agricole analyst Veronique Riches-Flores says the various plans put forward to date have each been built on a "rare complexity -- so complex, in fact, that they keep changing shape. "It just doesn't stand up to scrutiny," she added of moves including an appeal to China or Russia to buy into an as yet non-existent sister fund, or plans for money to be sliced up into insurance policies for specific countries facing problems raising finance on the open market. Beijing has said it will help but is looking for more information. Moscow has queried the logic of what has been proposed. Analysts such as the Bruegel Institute's Jean-Pisani Ferry point to weakness in the EFSF's constitution -- because any of the 17 eurozone governments can veto its actions. De Grauwe said that "if we want to keep the eurozone (intact), only the ECB can do it," a view backed by Riches-Flores. ECB chief Mario Draghi, however, will have none of this and on Friday he pushed back against heavy pressure to come to the rescue of the eurozone even as British Prime Minister David Cameron called for all eurozone institutions to defend the common currency. For Ferry, at the end of the day, the EFSF "is likely to stay in its initial form," seeing through the less troubled Irish and Portuguese bailout programmes and holding the line on Greece as it tries to claw its way out from under years of radical readjustment. That is the case too with a lesser-known European Financial Stability Mechanism (EFSM) at the level of the 27 European Union states, which has a 60-billion-euro limit and includes non-euro countries. It has primarily been focused on support alongside the International Monetary Fund for Hungary, itself back in the news this week as it seeks fresh help in the face of a stalled economy, strained finances and a falling currency.