I watched this clip from John Oliver's Last Week Tonight a few days ago and was surprised at just how many people seem to be against abortions in the US, so I went searching for numbers. I came across this page from Gallup which shows historical trends in the US abortion debate.
It appears that in 1996 the number of people identifying as "pro-life" rose dramatically while the number of people identifying as "pro-choice" decreased. This is such a large shift in a single year, that I assume something must have triggered it. What happened in 1996?
One version of the Partial-Birth Abortion Ban was introduced in 1995. It passed the House and Senate, but President Clinton vetoed it in 1996. The House then re-passed the bill with enough votes to override the veto but the Senate did not. The shift in perception likely occurred due to the media coverage and controversy surrounding the bill.