There isn't any way that we would do this, first and foremost because there isn't any need. Our bases in Qatar and Turkey are more than sufficient, and what Saudi Arabia is saying publicly and privately may be two different things.
"Well, GOLL-OLLL-LLEE! Looks like the infidels jest landed out in the middle of nowhere, Saudi Arabia, set themselves up an airport, flew in their troops, and, gosh-dern, we never laid eyes on 'em! Then they took down Saddam, and left via Basra. Shucks and all that. Looks like they done snookered us, y'all. Insh'allah, I reckon."