Most people's values are pragmatism based, not moral absolute based. Most people's values are based on "never close your options" or "sometimes you have to just plain do whatever it takes". That is why there has been no legislative progress whatsoever towards ending abortion despite numerous GOP presidents.
The American people accept that the Right to Life position is the moral one but the NARAL position is the practical and pragmatic one.
Unfortunately, I'm afraid you're correct. Most of the masses would deny that they favor abortion, but if it came down to it, and dear little Timmy or Buffy couldn't take that scholarship to go to college in order to look after their child, well...
This is moral laxity that, combined with political correctness, will destroy our nation.