Typically people talk about free trade as being more right-wing than left-wing. And support from politicians seems to back that up - Obama is having to work mostly with Republicans in Congress to pass the TPP. But apparently multiple polls find that, when it comes to voters, Democrats are more favorable toward free trade than Republicans. Could that just be a fluke? How could the voters and politicians misalign in this way?
Maybe this is just a strange alignment of each side's special interest groups. You can see how labor unions, who usually support Democrats, would be more opposed to free trade than corporations, who (at least relative to labor unions) align more with Republicans. If these two groups play really important roles in funding politicians, maybe that is why the politicians are split in the way they are, even if both special interest groups don't actually represent the views of the average voter.
And even though free trade can be thought of as a "free market" idea, I don't think most voters on either side really base their partisanship on economic ideas as much as we like to think. Maybe it makes sense that the average Republican voter is more opposed to free trade because you have to consider it from a nationalist/xenophobic perspective rather than an economic one.