No, the President shouldn't be able to borrow whatever he wants.
The debt ceiling mechanism might be an unnecessary anachronism and I'm not necessarily against doing away with it, but if nothing else, it can serve as a useful reminder to people about our ever-increasing debt. Maybe we should require a super-majority in Congress to approve any deficit-expanding appropriation instead.
"Well, it is one thing for Bill Clinton to say, I feel your pain. It is another thing for Barack Obama to say I feel your pain that I have caused." - George Will