Americans often view the European Union as a single entity, a unified collection of 27 member states as portrayed by its leaders. This veneer of unity masks deep-seated tensions and economic and political differences. The European debt crisis has exposed a great divide between economic powerhouses such as Germany and poorer neighbors such as Greece, currently sinking in a sea of debt. This has prompted Germany, backed by the French, to seek a new treaty to give the EU greater control over its members’ finances. Berlin and Paris are dreaming, however, if they think a piece of paper will keep the eurozone together.

The agreement reached in Brussels last week by leaders of all but one EU country (the United Kingdom) aims to create a European “fiscal union,” with binding limits on each country’s deficits, and penalties if they break them. It obligates them to submit their budgets to the EU for approval, forfeiting some of their sovereignty to Brussels’ unelected bureaucrats. The intergovernmental treaty also sets the stage for the new European Stability Mechanism, a permanent fund to replace the temporary bailout mechanism called the European Financial Stability Facility.

Monday’s opening markets and Moody's Investors Service’s criticism of the deal exposed just how fragile it is. It isn’t just that the U.K. balked when it couldn’t secure concessions protecting its financial services sector. Sweden, Hungary and the Czech Republic asked for time to consult their parliaments, and analysts predict Sweden and the Czech Republic won’t sign on. Moreover, Ireland and the Netherlands cannot sign on until they hold referendums to change their national constitutions.We’ve already seen Irish citizens reject one European treaty before being forced to accept it in a second vote under huge duress.

There have always been two Europes, a reality that the advocates of “ever closer union” choose to ignore. Germany, for example, thinks the common currency helps maintain its exports’ competitive price advantage within Europe. Less successful and more indebted countries such as Greece, Italy and Spain have been harmed by the euro, which allowed them to borrow at low rates that masked their debt. Now that Germany insists on greater budgetary austerity, that game is up. Not letting the fiscal crisis go to waste, Germany is not asking just Greece for budgetary austerity; it is demanding it across the entire European Union.

This is a far bigger matter than whether Greece or Italy can pay their debts. It is calling for the equivalent of a federated fiscal state for all of Europe. Many will see that as Germany’s bid for fiscal control of the EU. Germany and France, the architects of the single currency, have a great deal of economic and political capital invested in averting its failure.

It is hard to imagine this plan working. It’s difficult enough for democratic governments to deliver bitter economic medicine to their people. It’s harder still, if not politically impossible, for that medicine to be delivered by bureaucrats in far-away Brussels who appear to dance to the tune of German bankers.

The euro never should have been extended to countries like Greece. At the time of its EU entry, Greece failed to meet the debt criteria for membership, but everyone chose to ignore it. Now that Greece and others are in, everyone acts as though Europe will collapse into chaos if someone leaves the eurozone. This is a huge exaggeration. No doubt there would be much Sturm und Drang over any defections, but a two-tiered system — one for countries that can afford the euro and another for those that cannot — is more in line with reality than the current fiction of a single currency zone.

Whether the current eurozone survives is an open question. But the proposed fiscal union is unlikely ever to be fully implemented. The European Union will have to come to terms with economic reality and accept that a monolithic fiscal union is not possible.

Kim R. Holmes, a former assistant secretary of state, is a vice president at the Heritage Foundation