And that's the funny thing about solvency. As long as investors give you low interest rates, all is well. If they decide you will be insolvent, bond rates rise, resulting in a self-fulfilling prophesy where you actually become insolvent.
Solvency is of course inversely correlated to debt to GDP ratio, but there are tons of other actions at work.
The US debt to GDP ratio is rapidly approaching 100%
http://www.usgovernmentspending.com/federal_debt_chart.html
Once it hits 100% it's only a short walk to becoming a country not a lot unlike Greece:
http://www.tradingeconomics.com/greece/government-debt-to-gd...