It's not just Southwest that would fight it.
Ya'll have to remember Texas politics. If this thing gets ANY traction, Herb Kelleher's old business, Southwest Airlines, will do everything they can, with their impressive political clout, to squelch this project.
There are legions of companies that make their money from maintaining and expanding our highways, tollways, and related infrastructure that would eagerly join Southwest.
To be perfectly frank I don't think this project is going anywhere unless and until they have buy-in from the agencies and groups who have a vested interest in the status quo.