Treasury Secretary Janet Yellen implored Congress to "protect the full faith and credit of the United States" or face imposition of "extraordinary measures."
I'm expecting Trump will refuse to raise the limit unless he's personally enriched. My personal guess is that at some point in this term he's going to try to take out a large personal loan backed by the US economy. Probably by eliminating the debt ceiling and then just printing money for himself.
If Paul Krugman and Rashida Talib ever liked this idea as a workaround for GOP obstructionism, then there's not a high likelihood of it happening once the new Congress is in office on Jan 3.