The president, flanked by Secretary of State John Kerry and vice President Joe Biden, down played the claimed economic benefits of the pipeline, arguing it wouldn’t have lowered U.S. gas prices, created long-term jobs or reduced U.S. dependency on foreign energy.
wouldn’t have done means one would not have done something, whereas in reality it was done. In the article it means the pipeline would not have lowered U.S. gas prices.
would have done
is a fixed subjunctive construction.
It expresses a hypothesis about the past, meaning “intended to / was going to do something but didn’t”. When it is used, the condition that prevented the action (or would have led to it) is usually given.
Example 1:
If I had a chance, I would have set off on a journey round the world.
If I’d had the chance, I would have travelled around the world long ago. (It can also be read as a subjunctive about the present: “If I had the chance, I would travel around the world.”)
Example 2:
I would have told you the story about him, but you were not home.
I was going to tell you the story about him, but you weren’t home. (Given the condition “you weren’t home”, the story about him was not told.)
5. would have done with if
Example: If I hadn’t been busy that day, I would have gone there with them.
Had I not been busy that day, I would have gone there with them. (In fact, I was busy and so did not go.)
if can also be left out here
e.g.: I was busy that day. Otherwise I would have gone there with them.
I was busy that day; otherwise I would have joined them there.
6. In the article, lower is used as a verb, meaning “to reduce”.