There will be some tightening of the polls, but likely not within the margin of error. The polls have been far too stable in that regard. I know that there are some posters here flogging the outlier polls, but they are apt to flog anything that gives them pleasure, even if it is based on fantasy.
I think your basic premise is flawed. The policies being put forth by progressive elements of the Democratic party are popular, nationally. I think you've missed the boat. It is quite likely that more progressive policies will
increase Biden's popularity. When one's view is constricted to party-centric sources of information, one can get a skewed perception of what is "popular".
For some perspective,
Pew Center.