It is true that some giant corporations pay no income taxes at all on the huge profits. Others have moved to low tax countries to avoid paying U.S. taxes.
To fix both of those problems, President Biden has proposed (and the G7 nations have agreed to) a minimum tax of 15% on corporations no matter where they are headquartered.
As the chart shows, that idea is very popular with the U.S. public. No group opposes it, and even Republicans have a plurality supporting it.