A Hollywood Writer Guy predicts the script:

I was going to hold off on this, but since you brought it up again today, I’ll tell you exactly how they’re going to show the Geena Davis character’s “independence” on that show.
Either late in the first episode or early in the second, there will be a very dramatic scene where Geena Davis goes against the legislative wishes of a group of Dems and a group of Republicans – thus showing how she’s going to “think for herself” and giving the shows producers a chance to say, “See?
She’s non-partisan!”
But watch carefully. The Republicans will be advocating typical conservative causes: lower taxes and oil exploration, probably. And the Democrats will be advocating… less high-profile conservative
causes: say, school-choice and tort reform. The average viewer won’t notice the sleight-of-hand. But the pracitcal result will be a “non-partisan”
“centrist” and “independent” President speaking forcefully, movingly and brilliantly against four conservative issues.