Considering that Third Way is a Koch Founded & Funded lobby to promote neo-liberal, pro-corporation, conservative policies, of course they would be opposed to Democratic Socialism.
theintercept.com/2019/08/13/k...
Koch Industries secretly financed a 2007 report by Third Way titled “Why Lou Dobbs is Winning” — to promote the free trade agenda to liberals.
I get not wanting far left candidates to win but if the big “stab in the back” narrative for 2016/2024 is that third party voters/couch voters helped Trump win, this would only make the situation worse and with down-ballot repercussions.