Let's assume the United States goes over the fiscal cliff next year — that is to say, the Bush tax cuts expire and the big domestic spending cuts from the sequester kick in. This would be the single largest act of debt reduction in American history, cutting some $1.1 trillion from the deficit in the next two years.

(Brendan Hoffman - BLOOMBERG)

So you'd think that, if Congress and the White House can't make a deal and just let the fiscal cliff hit, we won't have to worry about another messy, potentially catastrophic fight to raise the debt ceiling, right? America's debt problems would be solved?

Wrong. Budget experts say that no matter what Congress and President Obama decide to do about the fiscal cliff this winter, the national debt will keep rising and the U.S. government will soon hit its borrowing limit. So, even if there's no fiscal cliff deal — and taxes go up, spending gets cut — House Republicans will still have to agree to raise the debt ceiling. Otherwise, we could see another financial panic.

The Treasury Department has said that it will reach its $16.4 trillion borrowing limit by the end of this year. In theory, the government can stave off hitting the ceiling until February or so by juggling around payments and taking "extraordinary measures." But, eventually, the government would no longer be able to borrow enough money to pay its bills. Crisis would set in.

Now, what happens if the two sides can't agree to a deal next month and we get that $1.1 trillion in deficit reduction? That still doesn't change much. "Going over the fiscal cliff will not avoid the need for a debt limit increase," says Donald Marron of the nonpartisan Tax Policy Center. "A bunch of the extra revenue and spending cuts are backloaded [i.e., smaller in the early party of next year and larger in late 2013 and early 2014]. More importantly, we will still be running deficits and racking up debt."

As the Congressional Budget Office explained in its August report, even if we hit the fiscal cliff and cut $1.1 trillion from the debt, the federal government will still run tiny deficits in 2013 and 2014 (that's the dark green scenario below). That means the the federal government will still need to raise its borrowing limit:

What's more, as Paul Van de Water of the nonpartisan Center on Budget and Policy Priorities explains, the Medicare and Social Security trust funds will grow by about $140 billion next year, which counts toward the legal borrowing limit. "Whether or not we go over the fiscal cliff, it will not have any appreciable effect on when we hit the debt ceiling," Van de Water says. At best, the Treasury Department might get a few extra weeks before hitting the ceiling. Not months.

Many observers have argued that Obama has all the leverage in the fiscal cliff negotiations. If he simply vetoes any deal Congress puts forward, then we hit the cliff on New Year's Day. Tax rates go back to their Clinton-era levels. Military spending gets slashed crudely. At that point, Republicans in the House and Senate will have to negotiate a new deal if they want to avoid making the changes permanent. So, the thinking goes, if Obama does nothing, he wins.

But that ignores the fact that Republicans have leverage, too. Even in this scenario, they can always refuse to raise the debt ceiling — as they threatened to do back in the summer of 2011. True, that could cause a lot of financial panic and chaos. Last year, the debt-ceiling standoff prompted the downgrading of America's credit rating. But Republicans used their threat to wring budget concessions from the White House. There's a possibility that could happen again. For more on that, see Annie Lowrey's report in the New York Times.

So whatever happens on taxes and spending during this upcoming lame-duck session, there's no way to escape the debt-ceiling question