I suspect the loudest voices would be from the automakers and dealerships, who make their biggest margin from SUVs and oversized trucks. They have powerful lobbyists and spend a lot on PR, so it often seems like their anti-transit, anti-pedestrian positions are more popular than they are.
I'd love to see a real grassroots effort to tax (toll?) based on GVWR or vehicle length. It would be met with tremendous opposition by special interests, but I could see it succeeding in the right environment. Maybe it could be framed as a rebate for small vehicles, rather than a tax on large ones.