The specific effects are local to the business. Broadly, the business will be affected by the global economic environment, making everything from raising money to executing sales more difficult.

Personally, I had an interent startup that went through a lot of challenges due to the financial crisis in 2008, even though we weren't in finance or even the US. But it made the funding environment so bad we had to change plans for some time.

The current tech market is stronger than most other segments, but don't get too comfortable. Internet businesses aren't divorced from real world economics.

Do you mean "how much a 'regional' crisis affects an internet business based in the US"?

I'm pretty sure that if this leads to a break up or two-tier Eurozone, then it is going to touch every business, every where, because economies are like kids at school -- once one gets sick it passes it on to all the others. It's certainly going to affect everyone in Europe, even those that aren't in the €. It's going to affect exchange rates. It's going to affect the ability of many people to buy your goods. And so on...