The Clintons are always associated with DLC (Democratic Leadership Council?), a centrist organization. Remember Bill Clinton is for all intents and purposes a Southern Democrat, so he is a close to a blue dog democratic president. Hillary Clinton luckily chose to be Senator of NY (which is a cold political move, esp. when you account for political polarization), she has moved to the Left when tides are that way. Hillary was a staunch centrist during Bush presidency including being very corporate friendly (and still is). Other than abortion rights, Hillary was all over in many issues, including crime, welfare, immigration etc. Her cold ambition fizzled in front of an aspirational candidacy of Obama and now, the D party moved to Left and Bernie pulled it to more Left, so she will play along with it. Hillary Clinton is architect of TPP in its current form, at it is politically expedient for her to deny it. The Clintons were always centrist, that is why Chelsea Clinton was on the board of IAC (pretty sure, its the last name, not her talents). The whole definition of Centrism esp. in a very ideological Political world, many times looks like Opportunism, and many Centrist leaders through out the world, ascend not with Philosophical fidelity but with carefully building a Personality following.

The president doesn't have legislative authority, and cannot pass either pro-gun or anti-abortion laws.

All they can do is, like Obama did with Obamacare, run what is essentially an advertising/pressure campaign to get something passed.