The whole world is watching while Greece decides between two unpleasant alternatives.  Will it further tighten its belt in order to stay in the Eurozone?  Or will it default on its massive debt, reintroduce the drachma and go through a severe recession likely accompanied by hyperinflation?   Greece has put itself into this precarious position by accumulating a debt of 180% of GDP.  It’s current situation would be much worse if it were not getting by with the low interest rate of 1.7% from the European Central Bank.
Compare Greece (see chart above) with the U.S. debt situation.  Our current public debt (on which we pay interest) is 74% of GDP.  This is the highest it has been since the end of WWII.  And, thanks to Federal Reserve policy, we are now paying an historically low interest rate of 1.7% on this debt.
The problem is that (under current policy) our debt will keep growing larger and larger until, by 2080, it would reach the enormous level of 270 % of GDP.  Our very low interest rate level of 1.7% will almost surely rise in the near future to a more normal level of 5%.  As interest rates do begin to rise, and long before the debt reaches 270%, interest payments on the debt will have increased to a much higher level, crowding out other spending.
Notice that, according to the above chart, our debt will reach the Greek level of 180% around the year 2055.  But with higher interest rates, it would be exceedingly reckless to assume that we won’t arrive at Greece’s currently perilous state much sooner than that.
Understanding that we have a very serious long term debt problem, it is imperative to begin to address it now, because the longer we wait:

• the older our population gets
• the higher the debt will rise
• the less time we’ll have to phase in changes
• the slower our economy will grow, and
• the fewer tools we will have to fix it

The answer to the question in the title is: Yes, we could easily end up like Greece if we are foolish enough to postpone action on our own debt problem for much longer.