Earlier in the briefing, Carney responded to questions about the coin option without directly commenting on the idea's merits, instead saying that the only viable option for dealing with the debt limit was for Congress to raise it. "The option here is for Congress to pay its bills, bills that have already been racked up," Carney said. Carney added that there is "no alternative" other than for Congress to raise the debt limit and that the administration does not have a "plan B."
On the surface, that may have seemed like a dismissive answer, but in light of his subsequent referral of questions to the Treasury Department, it seems more like an effort to to sidestep the question.
Moreover, whether Carney is aware of it or not, his answer was fully consistent with the coin idea. That's because even proponents of the coin believe Congress must ultimately raise the debt limit. Yes, minting the coin would buy time—perhaps quite a long time—before we hit the debt limit, but eventually it would need to be converted into debt. For that to happen, Congress would need to raise the debt limit. In other words, the coin wouldn't eliminate the debt limit—it would just postpone its impact until such time as a non-crazy Congress were elected.
While he sidestepped the coin, Carney flatly ruled out the idea that the 14th Amendment makes the debt limit itself unconstitutional. He also repeatedly said that under no circumstance would the president negotiate over whether or not Congress must ultimately raise the limit.