Who signed NAFTA?
That was a Republican-appealing thing Clinton did just like his welfare reform.
It's true that Clinton signed it, but not to appeal to Republicans. Clinton was one of the
New Democrats—a movement that fomented Third Way politics in the Democratic Party in response to its impotence during the Reagan administration, as implemented by the
DLC.
In a sense, political parties do not choose their positions at all. As motivated by the
median voter theorem, for any given issue, one party's position must always be just to the left of that of the median voter, and the other party's position must always be just to the right. For any given issue, neither party can switch their position to the other side of the median, because voters who find that issue most important will switch (to, e.g., apathy, a single issue party, the other party, etc.) Furthermore, people's views on different issues tend to be clustered into left or right. As long as this clustering exists, the optimal strategy is fully determined: one party must take the views just to the left of the median on every issue, and the other party must take the views just to the right.
eta: tl;dr: In a two-party system, there's no choice but for one party to be a little bit to the left on everything, and for the other party to be a little bit to the right.