No, but Allan Sloan in the Washington Post today thinks it can, or maybe it can. He proposes that Treasury borrow $200 billion in US government securities from China to use to continue to pay bills if we hit the ceiling, thereby supposedly overcoming dumb gridlocks that should not be happening and have led to such stupidities as the current "fiscal cliff." Sloan modestly calls this the "Sloan Strategem" (Ahem, rule against people naming things for themselves holds here, ahem!)
But the answer is no. Treasury already has a bunch of delaying mechanisms that hold off the moment of truth for several weeks. We saw that in 2011, when we breezed past technical bankruptcy in June only to fact it in early Augusst when the fiscal cliff got cooked up. This device would only add some other arbitrary amount of time that would simply delay the moment of blackmail reckoning.
The answer is to abolish the debt ceiling. People ranging from Bill Clinton through Bruce Bartlett to me and a lot of others have argued that the debt ceiling is unconstitutional on multiple grounds, quite aside from being bizarre and self-contradictory, actually incoherent. Obama should bite the bullet when it next comes really due, and declare it unconstitutional. I bet the markets will go up if he does so, although there will of course be a Supreme Court case on the matter. But better to fight that fight than to be set up to constantly have to deal with these blackmail threats that the House Tea Partiers have made it clear they will continue to impose repeatedly, no matter what comes out of the current fiscal cliff negotiations, which may well be things that voters most definitely did not vote for in this recent election and should not be put into place.