"Three yards and a cloud of dust" is an American football idiom (usually attributed to the famous Ohio State coach Woody Hayes.) Instead of having his players throw a long pass and possibly gain many yards at a time, Hayes preferred to have them keep the ball close to the ground and move in small increments instead.
In the passage you quoted, it appears that President Bush isn't taking any chances with long shots, or impulsive decisions. He is being conservative and making slow, short-range decisions.
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