The various oil companies don't really need Presidential encouragement. They do what they do based on profits obviously. They got slammed last year and shut things down as quickly as they could. They are restarting now, it takes some time and demand got out ahead of production, globally. I surmise OPEC doesn't want to open the spigots, which they could do quickly, because they could find they had done that just as demand eased and supply overall increased. US production would be slower to increase in any event with any President.
We consume about 20 million barrels a day, which is an astounding figure really and shows the difficulty of replacing that with ... something else. A barrel is about 44 gal.