The cost of insuring Spanish government debt climbed above 3% this month for the first time. Credit default swaps referencing 5-year Spanish government bonds traded at 340 basis points Wednesday, according to CMA data, meaning it costs $340,000 annually to protect $10 million of Spanish debt against default.

That spread has tripled over the past two years, as governments have started taking on the risks that were initially shouldered by overstretched banks.

But more important, according to a post Wednesday by the Center of Geoeconomic Studies at the Council on Foreign Relations, is a possible relationship between the level of the sovereign CDS spread and the effect on foreign bank depositors.

The CFR blog post points out that deposits started flowing out of Irish banks in early 2009 when the nation’s CDS spread widened out beyond 3%. The spread quickly contracted and foreigners resumed putting their money in the country’s banks, as dodgy as they may have appeared, evidently banking on the strength of the government deposit guarantee.

But as the cost of the Irish bank bailout soared late last year, the Irish sovereign CDS spread surged past 3% again, and foreign deposits resumed flowing out.

It is that flow that makes some investors think 2011 will be the year of the European bank run, starting in Ireland – whose CDS spreads now exceed 6% — and moving on to Portugal (5%) and then, perhaps, much bigger Spain.

Of course, it is early yet to say there will be a run on Spain’s  banks. While Spain and Ireland both had huge property bubbles,  Spain’s biggest banks, Santander (STD) and Banco Bilbao (BBVA), have substantial international businesses and thus appear to be in much better shape than their Irish counterparts, such as the fraud-ridden Anglo Irish or the simply deflated Allied Irish (AIG).

The bad news is that there have been signs of a deposit pricing war that could add to the stress on the smaller regional banks, which are seen as the weak link in the system. There are few indications the government is moving aggressively to clean up the bad loans everyone knows are out there.

Even if all goes well, the Spanish banking system is going to need time to earn its way out of years of property-lending misery. But if deposits start fleeing the country in earnest, the government will need to step in with costly actions, such as mergers and recapitalizations and takeovers.

And as the Irish experience shows, a rising tab for taxpayer support of the banks isn’t a recipe for making anyone happy — let alone for keeping money from heading for the exits.