Speaking to business leaders at the White House, Mr Clinton declared his "profound outrage" at an "act of cowardice" which left one crew member of Amtrak's transcontinental Sunset Limited train dead and 80 people injured. But, his aides insisted, the President had not decided the attack was an act of terrorism. "That is a conclusion for law enforcement agencies to reach," said the White House spokesman, Mike McCurry.
As the FBI took over, two theories predominated. The most popular was that, as suggested by the references to Waco and Ruby Ridge in the two notes left near the wreck by the "Sons of Gestapo", the derailment followed the pattern of April's bombing of the Federal building in Oklahoma City - an act of revenge for the two attacks by government agents on isolationist movements.
The second theory owed less to the notes than to the nature of the sabotage, which showed at least a rudimentary knowledge of railways. Hence, this view goes, the culprit could have been a disgruntled former employee of Amtrak, the government-subsidised company operating the Sunset Limited and other long-distance passenger services.
Yesterday Klanwatch, an organisation that tracks hate groups, said it had no record of the "Sons of Gestapo". But, Klanwatch's director, Joe Roy, noted: "It's not unusual for a cell of a larger group to take an alias when it branches out. Or it could have been a solo individual with a grudge, trying to blame it on the militias."
The FBI is pursuing both possibilities, delving anew into the shady world of the citizens' militias - the bulk of them harmless, but a few composed of hard-core extremists bent on the destruction of the federal state.
On one point, however, he and specialists are agreed: Arizona, with its anarchic Wild West past, its proven connections with the militias and frequent appearances in the tale of Timothy McVeigh, who is the chief suspect in the Oklahoma City blast, is a natural breeding ground for such incidents.
Inevitably, new questions are being raised about Amtrak's safety - just as the railway is fighting to stave off further cuts in its funding by the Republican Congress.
Amtrak has suffered a number of accidents in the last few years, most lethally in 1993 when the Sunset Limited, this time heading east, plunged off a bridge into an Alabama lake, drowning 47 people.
Amtrak says that without resources for investment, its network will perforce grow more obsolete and less competitive. But Amtrak's chairman, Thomas Downs, insisted yesterday that the system was "100 per cent safe", and denied that the perpetrator was an embittered ex-employee.
"About 300,000 people" in the US knew enough about railways to have removed spikes fastening the rails to the sleepers, unbolted a plate between two sections of rail and then rewired the signal which would have warned of a gap in the track.
America's very size means that rail tracks can never be fully protected. The Sunset Limited's route covers 3,066 miles, the western third of them mostly empty desert. And one person could have sabotaged the track in 10 minutes, a railroad official said.