It's not the same, Jake. The US government controls its own monetary policy. For one example, the USG can print money (it actually doesn't print money, it just increases the size of the money supply by monetizing debt, but the metaphor is basically correct) to reduce debt. That causes inflation, and inflation has the interesting effect of reducing the relative amount of debt compared to the size of the economy, because debt doesn't inflate with prices and wages. Greece can't print Euros. If it could there wouldn't be a problem, at least not in Greece, but that is exactly what they're going to do with their own currency, and cause runaway inflation. That inflation will pare down debt and interest payments as a fraction of the Greek economy.
BTW, I just looked it up, and the interest on the federal debt is about $430 billion per year. While this is a grotesque amount, 63% of the defense budget, the entire federal budget is $3.8T, so interest expense isn't even close to being onerous yet. Interestingly, US Treasury auctions have generally been over-subscribed, since the USG is still considered to be far and away the safest place to stash huge sums of money in the world.