Rising debt levels can cause some investors to lose confidence in the government’s ability to pay its bills. They would demand substantially higher interest rates.

Higher rates would discourage businesses and consumers from borrowing, thereby slowing the economy. The government would collect less in taxes and spend more on unemployment benefits and other social programs.

That creates a vicious cycle like the one that has entrapped European countries such as Spain, Italy and Greece; Rates are rising, economies buckling, budget deficits widening and debts swelling. So far, that hasn’t happened to the United States.

Investors, worried about the troubles in Europe, have been eager to buy Treasury debt, allowing the federal government to borrow at historically low rates.

— THE FIX:

If he’s elected to a second term, Obama has pledged to reduce the government’s deficits over the next 10 years by about $4 trillion. Obama says he would reduce the growth of federal spending — slowly, to avoid triggering another recession. He also wants to end the Bush-era tax cuts on income that exceeds $200,000 people for single taxpayers and $250,000 for couples.

Republican challenger Mitt Romney says he would also reduce spending growth by capping it at 20 percent of the economy by 2016. In 2012, spending has accounted for about 23 percent of the economy.

Romney would preserve the Bush-era income tax cuts for all taxpayers, regardless of how much they earn. The economy is too weak to raise taxes on anyone, Romney has argued.

He says his plan to cut income tax rates for everyone by an additional 20 percent would help produce more tax revenue. And he says he would reduce the deficit in part by curbing some tax loopholes and deductions.

Complicating the political options is a crisis that Congress must first resolve: A budget deadlock could send the economy over a ‘‘fiscal cliff’’ next year, when tax increases and deep spending cuts will take effect unless a budget deal is reached.