From 1933 to 2009, fiscally conservative types used to say things like, "The national debt is a problem," and the more knowledgeable among us would laugh and say, "It's not a problem at all! We owe it to ourselves!" Steven Landsburg has a chapter of his book The Armchair Economist about how the national debt only looks bad when you don't understand what you're talking about.
In 2009, we saw the return of the sovereign debt crisis. It turns out national debts do matter. This made some fiscally conservative types uneasy about the large amount of American government debt held by China. "Well," laughed the more knowledgeable among us, "national debts matter for small countries. But you don't really think China's going to take over if we default, do you? That's preposterous!"
This year, we are seeing the European Union (the largest government there is, based on GDP size) start into a sovereign debt crisis. As Europe tries to find a way to pass around the bailout bill and somehow have it disappear in the process, China has come up as a possibility. Some fiscally conservative types question how independent EU policy will be when they are on the China payroll. French President Nicolas Sarkozy dismisses thus: "our independence will in no way be put into question by this." And then the EU delegation to China is presented a series of concessions China would like. They didn't give in to them now, but once French bonds get over 5%, they will.
Of course you lose your independence when you are indebted to someone. That was why non-landholders couldn't vote in a republic. The basic unit was not the individual, but the economic interest. One economic interest, one vote. (It also keeps the voters from stealing so much if they already have stuff themselves, and have stuff that other voters can steal right back.)
Ultimately, the final response to any lingering sovereign debt crisis is a loss of independence. Greece thinks they've already experienced this (but the reality is that it'll really be coming next year). Newfoundland lost its independence when the government went bankrupt. In Georgia, Campbell County and Milton County ceased to exist in response to economic conditions. These things have happened before, and they will happen again.
And it's not a bad thing, actually. Bankrupt companies are evidence of the failure of their directors, and their resources are sold to non-failure directors. We're better off having non-failures control more resources than failures do. The same thing will happen at a geopolitical level. If China ends up reducing America to a protectorate, it will be the result of the failure of the American government, and I couldn't very well support free market principles in one arena while saying failures should be insulated from their decisions' consequences in the arena of government.