In addition to the calls for universal healthcare, there is a national campaign for a Homes Guarantee. I think there will be pressure on the federal government to improve the housing social safety net including improving and expanding public housing. Public housing is stigmatized in the United States, but in other countries (like Singapore) public housing is mixed-income, safe and high quality. I have my doubts about the Federal government's ability to execute this effectively, but if we could mimic Singapore or Austria it could be beneficial for society. Important to note also, that in these countries, people can still buy and sell real estate and people can choose to rent from private landlords. Public and privately-owned housing exist in tandem.
In terms of the rental market, I think there will be an expansion of C-class apartments and rental housing. As residential lending standards tighten (higher down-payments, higher credit score requirements) I believe we'll see an increase in renters and decrease in home ownership.