But with borrowing costs for Spain climbing close to the 6% level that has repeatedly signalled danger throughout the crisis, most euro-watchers expect Rajoy to be forced to accept a package of aid, along with the strict list of terms and conditions that would imply.
Meanwhile, Moody's is expected to deliver its verdict on Spain's sovereign debt rating in the coming days, and a downgrade could just be the catalyst the markets need to drive up Madrid's borrowing costs to dangerous levels.
Last week's Spanish budget, which contained numerous new spending cuts and reform measures and won the approval of the European commission, was widely seen as a bid to pre-empt any extra austerity measures that Spain's creditors might be likely to impose.
A bailout would allow European Central Bank president Mario Draghi to deploy his "outright monetary transactions" and make unlimited purchases of Spain's bonds. But going cap in hand to the troika – the ECB, European commission and International Monetary Fund – would still be a deep political humiliation for Rajoy, at a time when Spain's regional leaders are jockeying for independence and sky-high unemployment of more than 25% is imposing an excruciating cost on the population.
Even if Rajoy can drive through the measures needed to secure a bailout in the face of mass public opposition, hold the Spanish state together despite growing separatist sentiment and rebuild the country's battered banks, the road back to prosperity looks like a long, hard one – and that's already a lot of ifs.
Rumour has it in Brussels that eurozone politicians have sworn not to push Greece out until after Barack Obama is safely back in the White House. But few analysts believe it has a long-term future in the single currency.
After fraught negotiations that stretched on all summer, the coalition government, led by Antonis Samaras, appeared last week to have reached agreement on a new package of cuts, which it hopes will satisfy the demands of the troika.
But Greece's economy remains in a wrenching recession, and it looks likely they will continue to miss the goals set by international lenders, even if the next €31bn (£24.7bn) disbursement from its bailout fund is released. Eventually, Greece's partners may decide to let it go – especially if they believe they have elected a solid firewall that would prevent a "Grexit", as it's known, creating a devastating chain reaction in financial markets.
And Greece could yet decide to leave of its own accord, if domestic political pressure becomes too intense. With Samaras elected on a promise he would exact concessions from the country's creditors, the political reaction to a fresh round of cuts from a population already scarred by the downturn is likely to be furious. Protesters threw Molotov cocktails at riot police at a protest during last week's general strike, the latest of many as the workforce has endured cuts in benefits, wages, pensions and public services to meet the troika's deficit targets.
In theory, the "internal devaluation" Greece is going through is aimed at making the country's goods more competitive on world markets by cutting the cost of production. But there is little sign that growth is about to be restored.
"If you look at what Greece is going through, it's comparable with the Great Depression," says Dario Perkins of Lombard Street Research, pointing out that economic output has already plunged an extraordinary 20% since the start of the crisis. "The US Great Depression didn't end because of austerity, it ended because they left the gold standard and they had a massive devaluation, and because fiscal policy was moving in the right direction."
One of the things that most alarmed Europe's financial markets last week was the outcome of an obscure meeting in Helsinki that suggested the single currency's paymasters have decided to play hardball.
Finance ministers from the Netherlands, Germany and Finland – the eurozone's paymasters, and also its most hardline members – gathered for talks in the Finnish capital and issued a statement clarifying the eurozone rescue deal that was reached after make-or-break talks in June.
At the time, the agreement appeared to mark a positive departure in the crisis, helping to sever the connection between the balance sheets of sickly banks and the finances of states. It was agreed – or so it appeared – that the eurozone bailout fund, the European Stability Mechanism (ESM), would be allowed to inject money directly into ailing banks in eurozone countries.
That would prevent their governments from having to apply for a full-blown bailout, with all the attendant misery of troika inspections, and halt the vicious circle in which bank bailouts shift losses onto the public finances and weaken public finances by depressing the value of the government bonds that are the banks' main source of capital.
However, after last week's discussions in Helsinki, the canny northern Europeans spelt out their conditions. Before the ESM can bail out banks, they insisted that the eurozone-wide banking union must be "established" and its "effectiveness… determined" – which is a tough hurdle, since the plan so far remains a glint in José Manuel Barroso's eye.
More importantly, they insisted that "legacy assets" – that is, all the dodgy loans from the credit crisis era, must remain "the responsibility of national authorities".
At a stroke, they seemed to dash Ireland's hopes of receiving help from its eurozone neighbours for the cost of its massive banking bailout and undermine Spain's hopes of repairing its financial sector without Madrid going cap in hand to the troika.
But most damagingly, the announcement from Helsinki underlined the fact that, in the long-running eurozone crisis, the devil is always in the detail.
With Spain still firmly in the markets' crosshairs, Italy's moment of danger appeared to have passed, at least for the time being. But after 30,000 strikers forced the closure of the Colosseum on Friday as they marched in Rome against the government's public sector cuts, political support for austerity in the eurozone's third-largest economy is looking increasingly fragile.
A year into a deep recession, the technocratic prime minister Mario Monti, installed last November after intense pressure from the markets and eurozone politicians helped force Silvio Berlusconi out of office, is struggling to meet his budget goals. His support is also fading – though he said last week that he might agree to stay on if elections, due to be held in the spring, failed to yield a definitive result. He has acknowledged the concerns of protesters, saying his austerity policies have subjected the public to an "unprecedented amount of sacrifices".
When the ECB president Mario Draghi announced his policy of "outright monetary transactions" – or OMT – the expectation in financial markets was that Italy would follow Spain in asking for an official EU bailout so that it could benefit from the scheme, which is designed to bring down weaker governments' borrowing costs by buying their bonds.
But that would be a severe political humiliation – and, what's worse, it is not even clear that Europe has the money. As Karen Guinand of the bank Lombard Odier put it in a research note last week: "If and when Spain does appeal for help, another problem will then emerge: much of the EFSF/ESM [bailout fund] resources would probably be used up … leaving little for Italy."
Once a Spanish bailout happens – and most analysts now believe it is a case of when, not if – attention will inevitably turn to Italy, just as the country gears up for a general election in which Berlusconi and his supporters are expected to run on an anti-euro ticket. The former prime minister last week described the single currency as a "big swindle"; staying inside the euro will require more painful sacrifices, and Italians may decide that they have had enough.
Even if all the other pieces fall into place – the Spanish bailout, the latest tranche of the Greek rescue, Mario Draghi's bond-buying splurge – there remains the question of whether the widely diverging fortunes of the eurozone's economies can be brought closer together.
Europe's statistical agency, Eurostat, expects the eurozone economy to contract by 0.3% in 2012, and expand by a paltry 1% next year.
But that average disguises a sharp divide: while the powerhouse of Germany continues to expand – though at a less healthy pace than in the last 12 months – much of the rest of the single currency area is trapped in a deep recession, unable to compete with the wealthy economies of the north, where, certainly in Germany's case, falling real wages over a number of years have created a super-competitive manufacturing sector.
"The bigger issue for us always is: does any of this address the underlying problems?" says Jonathan Loynes, European economist at Capital Economics.
"Even if the ECB comes out with all guns blazing, all it's doing is dealing with one of the symptoms: it's not reducing anyone's debts."
He fears that while Europe's politicians may be able to paper over the cracks with emergency bailouts in the short term, voters in Germany and the other "core" economies in the currency bloc may not be willing to countenance the large-scale financial transfers that would be necessary if Greece, Portugal and Spain were to be brought up to speed with the rest of the eurozone.
Dario Perkins of Lombard Street Research warns that public opinion in all the struggling economies – Portugal, Greece, Spain and Italy – is likely to become increasingly impatient if the universally prescribed recipe of austerity fails to improve people's lives. "You can't continue with no growth indefinitely: these are democracies."