I consider this ratio rather inconclusive, however it is cited so often as a key measure of a country's 'strength'...
Similar to how a D/E of a company is not as important as the interest it pays out as a % of its discretionary cash or debt maturity schedule and covenants, the debt to GDP of a country is rather ridiculous.
Denomination of a country's debt is important - most (if not all) of US's debt is in dollars which it can print as it pleases; also, refinancing will not be an issue as much as coupons payable will be.
Tenure profile is important... I read somewhere that France's dilemma is that most of its debt is short term in nature, therefore more pressure on it to refinance the moneys.
External / Internal debt: Even though Japan and India have substantial debt, much of it is held domestically and the demand for them is rather trustworty... Relative to that, a large chunk of American debt is held by foreigners who could possibly find different avenues for that money.
Also, non-governmental debt issuance (or liabilities - refer Ireland) is also an issue - something that is rarely addressed but is of substantial consequence.