I appreciate the acknowledgement ofthe 'No True Scotsman' trap. It is easy to define a side by its ideals (e.g., 'The Left is for the poor'), but the reality is that both sides muck it up the moment they take control.
Neither side actually supports the poor because both are funded by and literally are the wealthy masters. The evidence is in the trends/facts that for almost 50 years the wealth gap has only widened, regardless of who is in charge. At some point, we have to accept that the 'which side is right' argument is false.
Neither of the two major parties in US politics supports the poor.
Elsewhere there are broader choices in national politics.
eg: the current Prime Minister of Australia grew up with a single mother on a disability pension in council housing. His actions and politics are at least informed by real life experience as one of "the poor".