[WS:] This begs the question whether party "identities" are written in stone or are subject to political pressures from below. My hunch is that is a mixed bag, or to be more precise, about 1/4 of the former and 3/4 of the latter. That is to say, while parties have some parts of their identities that are relatively fixed over time, they are also in the business of winning elections, which makes them responsive to pressures from the public (however defined.)
The fact of the matter remains that left policies - by which I mean European style social-democrats and parties left of them - enjoy support of a rather tiny minority of the US electorate - around 5-6 percent judging from historical records (e.g. Debbs - who arguably represents the highest mark of left politics in the US received only 6% of the votes.) Contrary to opinions expressed by many leftists, the majorities of the US electorate do not vote for a "lesser evil" but for candidates who more-or-less reflect their own political views, as Hofstadter ("The American Political Tradition") aptly observed.
>From that POV, the main question is not how to establish a left party
in the US, but how to make left politics more acceptable to the US
voters. If the views of the US voters drift to the left, I am pretty
sure the question of a left party - whether a new brand name or a
'reformed' Democrat party - will be answered in some way.
Wojtek