The big fear is that this will reopen contagion channels, and make depositors in places like Spain and Italy nervous about their accounts.
Now if the tax doesn't pass parliament in Cyprus this week, then all bets are off, because the country could have a banking collapse.
But if it does, then there are some reasons to think this won't be the epic catastrophe that some are suspecting.
Here are two key points:
One is Cyprus' status as a haven for Russian offshore money — and why that makes Cyprus unique — is well known in Europe. It's why German politicians balked at a pure grant bailout, because it's an election year, and there's not much appetite to bail out oligarchs. The fact that this became an election-year political issue means the public grasps this angle, and so are likely to grasp why they're unlikely to get Cyprus'd.
Beyond that, this isn't like Lehman. In Lehman, the banks were actually allowed to fail, and the status of post-failure creditors was highly uncertain. Lehman was super-complex, and it was not clear at all how it would be resolved. In Cyprus there's no failure, and the status of creditors is clear. Depositors clipped. Done.
So the obvious avenues of contagion are not present.
Again, if the tax isn't passed, then all bets are off. And there could be political contagion channels (will Italy have a harder time forming a government?), but the idea of a wholesale bank run seems unlikely.