By the time it got to Bush, he could have stopped it by sending federal marshalls and enforcing the House's subpoena. The judge in Fla. was basically trying to kill a witness to a congressional investigation. He backed off from that, and the House leadership didn't have the juice to do anything without the White House behind it. It was Rove, I think, who blinked.
And bingo, the Dems were energized, the conservatives were demoralized, and we were left with the feeling that it could have turned out differently had someone with some gumption taken action. Like Reagan firing the AT controllers, it needed someone to step in and do what was right, and the country would rally around that kind of leadership. Instead, by shrinking away from leadership, and forcing us to watch her die a slow, terrible death, we all became a little less enthusiastic about GW Bush at that time. All except that small but vocal wing of the GOP that was for Terri's death--people like this guy on this thread who is going around calling people names.
Ignore the trolls.
You're right in your assessment of how things played out. A swamp judge weilded more power than the Executive and Legislative branches put together. And the liberals squeeled with delight.