While I disagree with him, I like the fact that he is referring to the consitutiton while making the argument. The 14th amendment dictates that debt must be paid. If a debt ceiling prevents the debt from getting paid, then the debt "ceiling" is illegal.
Basically, the constitution does not allow anyone to stop the US from defaulting on the debt. The implications of that are not clear cut.
Ultimately, the Republican party in general has little to stand on when it comes to not raising the debt limit. Ron Paul himself voted for 3 trillion+ in tax cuts (the Bush tax cuts) that have contributed to our national debt. Most of the current debt comes from Reagan and GWB, including federal reserve purchases which outside of QE2 started under Bush the second and only just completed under Obama.
By that, I mean, that the reason we have a debt is mostly due to "Republican" policy. The wars (2.3 trillion and counting), the increased military spending (about 1.5 trillion on top of that and counting), DHS (about 400 billion and counting), Medicare part D (100 billion and counting), no Child left behind, the Bush tax cuts (3 trillion and counting), etc. comprise a huge part of the national debt. Since Clinton, when the budget was balanced and the CBO predicted 10 years of a modest budget surplus, the only major Democratic spending initiatives have been the 600 billion dollar stimulus, the ~400 billion or so expansion of welfare past paid welfare, and the 900 billion in tax cuts which they endorsed in the stimulus and in the expansion of the Bush tax cuts. You can arguably include Bush-era policies that Obama and the Democrats have suddenly endorsed like the DHS and the wars.
Plan for eliminating the national debt in 10-20 years:
Specific cuts; defense spending: http://rolexian.wordpress.com/2011/01/03/more-detailed-look-a