Greeks actually pay more taxes, as a percentage of GDP, than Americans do (31% versus 27%). The main differences lie elsewhere, #1 being that the GDP that is taken out of is much lower, due to Greece having mostly a cottage-industry type economy (lots of small family businesses, few megacorps). That in turn has a lot of causes, some cultural, some historical, some due to excessively complex regulations (which have been streamlined in the past 10 years, but not fast enough).
The US is far from the path to debt free either - the difference with Greece is that they can print their own money. The US is trading low taxes against high inflation right now.
Except our inflation isn't particularly high at the moment in the US, we were undershooting our 2% target for a while then the Fed printed a bunch of money (because they can't bring the Fed Rate below the IOR Rate) and now we're on target again.
EDIT: The fact that we could print money to get out of debt if we needed to is a big part of why we don't need to, though.
