I talk with many on the left: support for late-term abortion is incredibly small, and rabidly vocal. Very similar to the trans bathroom issue years ago: most of the (at the time, tiny) trans community weren't the ones raising hell about it
It is small, but not that small. I read the other day that those that support no time limits on abortion are somewhere between 10-20% of the population (I forget exactly). Lots of politicians are in there. Just the other day that is what the gov of NYC said he wanted. That is the position of NARAL, with millions of members.
Most importantly, right now there are
no limits on abortion until birth in these states:
Alaska, Colorado, District of Columbia, New Hampshire, New Jersey, New Mexico, Oregon, and Vermont.