The National Debt goes up for two main reasons: Social Security and the Trade Deficit.
The Social Security "trust fund" is a bunch of T-bills, and represents the second largest chunk of the National Debt - $2.72 Trillion. Whenever they take in more social security payroll taxes than they pay out in benefits, they put the surplus into T-bills. Those T-bills are then counted as part of the National Debt.
In other words,
1. We owe this chunk of the National Debt to ourselves - to old people and sick people
2. The Social Security Payroll Tax is not really used for Social Security - it just goes right back into the general fund, and even worse, the general fund has to pay interest to Social Security, which means we're even more screwed than you thought.
The other reason the national debt keeps going up is due to the trade deficit.
We buy Chinese goods in Dollars. We pay them in Dollars. They can't use dollars in their domestic economy for anything - worthless paper to them. They'd have to plow the dollars into American goods to make use of them, but they don't do that. They don't buy enough of our stuff, so instead of stuffing that cash in a vault somewhere, they buy a bunch of T-bills so they can collect interest. That accounts for the largest chunk of the national debt, over 5 Trillion.
Important to note that, no matter what happens with spending, the national debt will continue to grow because of these two things. Blaming the national debt on spending alone is not accurate.
More reading and sources for my numbers are here.