Most people in the US would be happy with those arrangements. The abortion controversy in the US is manufactured - those opposing abortion focus their rhetoric almost entirely on second-and-third trimester abortion, those who support it focus their rhetoric almost entirely on first-trimester abortion, and both sides pretend the other side is talking about the same thing they're talking about.
The controversy, that is, is produced by the opposing sides asking different questions.
~70% of people don't care or want the first trimester to be legal (AFAIK it's legal in all states). ~65% want the second trimester to be illegal (no idea what the legal status is). ~80% want the last trimester to be illegal (It is illegal in all but 8 states).
~75% want abortion to be legal for medical reasons, regardless of trimester.
About 30% of the US population would be unhappy with the Swedish arrangement. http://www.gallup.com/poll/1576/abortion.aspx
Compare that to the manufactured controversy: http://townhall.com/tipsheet/guybenson/2014/03/10/cnn-poll-58-percent-of-americans-oppose-abortion-in-all-or-most-circumstances-n1806283
Most people in the US would be happy with those arrangements. The abortion controversy in the US is manufactured - those opposing abortion focus their rhetoric almost entirely on second-and-third trimester abortion, those who support it focus their rhetoric almost entirely on first-trimester abortion, and both sides pretend the other side is talking about the same thing they're talking about.
And yet look what happens when people try to bad third trimester abortions.
One of my favourite Less Wrong articles is Politics is the mindkiller. Part of the reason that political discussion so bad is the poor incentives - if you have little chance to change the outcome, then there is little reason to strive for truth or accuracy - but a large part of the reason is our pre-political attitudes and dispositions. I don't mean to suggest that there is a neat divide; clearly, there is a reflexive relation between the incentives within political discussion and our view of the appropriate purpose and scope of politics. Nevertheless, I think it's a useful distinction to make, and so I applaud the fact that Eliezer doesn't start his essays on the subject by talking about incentives, feedback or rational irrationality - instead he starts with the fact that our approach to politics is instinctively tribal.
This brings me to Joseph Bottum's excellent recent article in The American, The Post-Protestant Ethic and Spirit of America. This charts what he sees as the tribal changes within America that have shaped current attitudes to politics. I think it's best seen in conjunction with Arnold Kling's excellent The Three Languages of Politics; while Kling talks about the political language and rhetoric of modern American political groupings, Bottum's essay is more about the social changes that have led to these kinds of language and rhetoric.
Video of a related lecture can also be found here.