It all depends on how you ask the question. If you only ask a question like this one that is a yes or no, most people will say keep abortions, but if you give people a more nuanced set of questions to include an option to add more restrictions to abortions suddenly most Americans clearly want to add more restrictions:
The survey found that 81 percent of Americans and 66 percent of those who identify as pro-choice would restrict abortion to — at most — the first three months of pregnancy. Eighty two percent of women agree with that. The pollster says these findings have been consistent for the last eight years.
Even this story admit this, look at their wording:
Recent research from the Pew Research Center indicates that 69 percent of Americans — or 7 in 10 — say Roe v. Wade should not be completely overturned.
“completely overturned” is the key wording, you notice they never ask if people want more restrictions added to abortions because that answer would not help their agenda.