Because as the WH brief says, because of the FISA jurisdiction. You'll recall the complaints they had, previously, that either the WH wasn't first going to these courts, or when they did, the subjects of the surveillance got away. They are only on the phone for so long, or only on particular phones (apparently the bad guys switch off, a lot).
This surveillance is out of FISA jurisdiction because it is of conversations outside US borders (whether Bush remembers that we have national borders, is another matter). I suppose an amendment, when these matters are taken up again, might insist that the courts be apprised of the facts which otherwise would support a warrant. But it would be after the fact.
I agree with the bill, as far as it goes. These people have to move quickly to intercept conversations. And who knows what might be suggested, or even said?
Now if it were a matter of American citizens, with both calls inside our borders (again, Mr. Bush, we do have national borders), as much as I could see the benefit were either one or the other part of a terrorist cell, the law would probably demand a warrant, a court approved warrant.