No one seems to know exactly when the real US debt ceiling deadline is and what can be done to extend it. It depends on tax receipts, the timing of outlays and whatnot.
By declaring that he sees it as June 1 and also that it will take 72 hours to get a deal written up, he sets his deadline at Monday or Tuesday -- perhaps even earlier if he wants the Senate to have some time to wrangle.
In any case, this whole thing is a joke and always has been. The US isn't going to default.