Why is government debt level presented as ratio to GDP, not against government budget or revenue size? A country's public debt is often presented as ratio to GDP. For example, in Wikipedia, List of countries by public debt or National debt of the United States both use ratio or percentages of GDP.

Since government borrows the money in term of balancing budget and will have to repay using budget, shouldn't it make more sense to define the ratio against something related to the size of the budget, instead of the size of the whole economy? Someone pointed out to me that when seen this way, the debt ratio sounds more serious. For example, US public debt is ~18 trillion, which is slightly more than the annual GDP (this doesn't sound too bad), but actually roughly 6x government revenue in 2014 (~3 billion according to CIA World Factbook)
The ratio of government debt to GDP is a useful indicator because, broadly, the larger a country's GDP, the larger is the tax revenue the government could potentially raise to service the debt while maintaining other government expenditure at an acceptable level.  Thus a very high debt / GDP ratio would raise doubts about the government's ability to service the debt.

One reason why a larger GDP implies a larger potential tax revenue is that most of the transactions making up GDP from an income perspective, eg wages and salaries, company profits, could be taxed.  However, taxes could also be levied on items that are not part of GDP, eg capital values of property.  The more fundamental point, therefore, is that a larger GDP, again from an income perspective, tends to imply a larger aggregate ability to pay, out of that income, such taxes as may be levied by the government.

The government's ability to tax is also influenced by political factors and by the effectiveness of its tax collection, so the debt / GDP ratio can only be a crude indicator of ability to service debt.