The current debt limit is 14.294 trillion dollars. You can view the U.S. national debt here. Right now, it is showing the U.S. national debt and the U.S. public debt subject to limit. The debt subject to the limit is slightly lower. It is projected to hit the limit in mid-May, sometime next week.
If the debt ceiling is not raised, the government can keep things going for a few more months using accounting gimmicks. The politicians are good at accounting gimmicks. They can continue to run up debt a little while longer while not really counting it as debt.
Many of the politicians are screaming right now that refusing to raise the limit is not an option. They are wrong. It just isn't an option that they like. It would not necessarily mean default. It would mean that they would have to drastically cut spending. This is why the limit will be raised.
If you didn't have enough evidence already, the next few weeks should tell you all you need to know about the Republicans. They will demand a few spending cuts. The actual cuts will just be a small fraction of the total bloated federal budget. Both sides will compromise on more debt and more spending and the party will live to see another day.
It is even hard to judge your congressman by his individual vote. Congress has this trick of vote counting. They just need to come up with enough votes to raise the limit. They will allow some of their colleagues to vote "no" if they are fighting hard for reelection and they need to prove to the voters that they are tough on spending. The whole game is rigged.
Obama voted against raising the limit when he was a senator. He has now changed his tune. The Republicans (with a few exceptions) are frauds too. The Republicans have the majority in the House of Representatives right now and could refuse to raise the limit. This will not happen.
As a libertarian, I believe the federal government should sell off its assets and pay off its debts. Anything remaining should be repudiated. I understand this is a radical stance, even for a libertarian. But for any libertarian, you should at least be demanding that the limit be held where it is. This would force immediate and dramatic cuts. If the politicians started shutting down whole departments and dismantling the empire overseas, then the government could probably continue to pay interest on the debt and continue to hand out money for Social Security and Medicare, at least for now.
There is no hope of a balanced budget. It is going to take a crisis in the dollar. We will end up in a situation like Greece or we will end up with massive inflation and then we will end up like Greece. Until the American people make serious demands about drastically cutting spending, including entitlements, the military, education, and virtually everything else, then the politicians will continue to spend as long as the Fed keeps buying debt. This really isn't going to be a pretty ending.