Basically, the guy admits that he overstayed the terms of the Visa Waiver Program, but is arguing that the fact INS started processing his adjustment of status application gives him the right to stay in the U.S. until it's resolved:

> Culleton concedes he is removable under the VWP. Reply 10. But he argues that because USCIS accepted and began processing his adjustment of status application, he is entitled to due process protections in its fair adjudication. Id. at 9. The Fifth Circuit has foreclosed this very argument, reasoning that the VWP waiver includes a waiver of due process rights. See Mukasey, 555 F.3d at 462. And “[t]he fact that [Culleton] applied for an adjustment of status before the DHS issued its notice of removal is of no consequence.” Id.

Remember that the whole point of the Visa Waiver Program is that you're conceding up front that you're just visiting and aren't making a claim for asylum or whatever. The idea is that the U.S. makes it easy for you to enter, in return for you agreeing that the U.S. can easily deport you if you overstay.