The new prime ministers of France and Italy are challenging the pro-austerity consensus in Europe. Manuel Valls and Matteo Renzi are demanding more time for deficit-reduction in exchange for undertaking the economic reforms needed to make their countries more competitive. It promises to be the most open challenge to the policy consensus that drove the eurozone into its deepest depression yet.

The two men arrived at this position independently of each other, I have been assured. What unites them are angry electorates fed up with years of cuts. It is easy to understand the politics of this but the question remains of whether the resulting economics make sense. I fear they have not thought this through.

Italy’s 2014 deficit target stands at 2.6pc of gross domestic product. The Renzi government will almost certainly miss this target. Its economic programme consists of tax cuts for individuals and companies. The proposals for how they are financed are much less clear. Even the more relaxed French target of 3.6pc is off-track right now.

Are France and Italy right in stimulating their economies at this point? Step back and you notice there is something seriously weird about eurozone fiscal policy. When the economy was in recession, various governments imposed austerity. Now that the recession has ended, they start to relax policy. It is exactly the opposite of what they should have done. Decades of stability pacts, countercyclical budget rules and fiscal compacts are for the birds. We are back to the bad old days when fiscal policy is determined by how much cash the finance minister has in the pocket.

I blame austerity. It has destroyed so much economic output that it made debt sustainability harder - the exact opposite of what it was supposed to achieve.

Irate voters are now turning against incumbent politicians. In France, the National Front hopes to win the most votes in the European parliamentary elections in May. The Five Star Movement of Beppe Grillo is holding on to 25pc in the Italian polls. We should not underestimate the extent of the mood swing in the two countries.

A resumption of robust economic growth is a necessary condition for debt sustainability. By contrast, in a world with no growth and no inflation it would take a very brutal path of deficit reduction to get debt levels down to the agreed targets.

A slower pace of deficit-reduction might help a little. But a shift in monetary policy is what it takes to do the heavy lifting. Last week, the European Central Bank once again failed to act on the acute threat of disinflation. Instead, the central bankers got bogged down in a silly discussion about the impact of the timing of the Easter weekend on inflation, as though this had anything to do with a disinflationary trend that has been going on for nine months.

No matter what Mr Renzi achieves, his country would be headed for certain default if the eurozone’s future inflation rate were to fall from a previous average of 2pc to 1pc. Italy cannot afford the combination of Japanese-style debt levels, growth and inflation rates, and eurozone periphery-style interest rates - not even now when the bond spreads are much lower than they used to be.

The second critical prerequisite is a clean-up of the eurozone banking sector. At least 700bn euros are needed for this, according to a recent estimate. I am not holding my breath, and will judge the validity of a continuing clean-up exercise of bank balance sheet in terms of how close the announced result will come to that number. I would be surprised if it were more than 10pc.

What is likely to happen? My guess is that Mr Renzi and Mr Valls will secure a symbolic but not substantive concession. They may get some minor flexibility. This is how Europe works. You want 1pc, Germany says zero, and you end up a number like 0.1 or 0.2pc. This is not exactly the arithmetic average. Think of it as a political average. Also consider this: Germany and Finland have already protested against two previous rounds of relaxation of French and Spanish deficit targets. The air is getting thinner.

Just busting the budget in 2014 is therefore not a smart strategy. Mr Renzi and Mr Valls will need to go further and mount a broader challenge. They could, for example, have a go at the fiscal compact. From 2016 onwards it will require that each country reduce its current debt ratio to 60pc of GDP in 20 years. This is much tougher than a 3pc deficit ceiling. Italy, for example, will need to have a primary surplus — before interest payments — of at least 5pc on average for 20 years. I fail to see how that can be made to work.

So it all comes down to the ECB and its ability to prevent a sustained fall in inflation rates, and to French and Italian readiness to pick a fight with Germany and its northern allies. On either front, there is only talk, no action.