I think you have pinpointed the core issue.
Right-wing republican policies and ideas lends themselves to simple (but often wrong) models of explanation; "it is the fault of the immigrants; the poor; abortion is always immoral", etc. You get candidates that radiate confident leadership spewing simple talking points they believe in.
Left-wing, especially progressive, ideas are often rooted in insight into the incomplete understanding we have of the underlying complexities. People who navigate these ideas won't be as confident: "the cause is a bit of this and a bit of that; we don't really know, but research points at" etc. To confidently sell policies based on these ideas to voters requires a level of cognitive dissonance, and also opens for criticism on being indecisive.
How can we package left-wing ideas in a way that attracts voters who are swayed by simple ideas presented with absolut confidence?
Time travel as a sudden jump seems one of the least plausible implementations, since we have no idea how to do such jumps even in just space or forward in time; and allowing for it would break a lot of physics.
More plausible alternatives include a space-time bridge, meaning both sides can follow Earth's reference frame; or the Primer-type where one can reverse time in an isolated box in a way where you can only travel backwards along the Box' trajectory and you have to wait inside that box for some time while you move backwards in time along that trajectory.