It was bipartisan because the Democratic party swung rightwards (towards the center) on economic policy under Clinton with the said "Third way[1]", which combined being socially progressive with economic liberalism, i.e. cozying up to employers rather than workers, which was the Democratic party's former schtick until they lost a couple of presidential elections in a row through the 1980s.
It wasn’t quite bipartisan. Only a minority of democrats in the house (108 of 258) voted for nafta for example. Large swaths of the Democratic Party opposed free trade until Obama.
I thought the support was bipartisan? For instance: https://en.wikipedia.org/wiki/United_States%E2%80%93China_Re...