I would guess the Nazgul, since they're enough to freeze the blood of far stronger men than Butterbur. Though, after their experience at the Prancing Pony, the Nazgul are a lot closer to him than a day's march; more like ten minutes' march (ride) or so.
He could also just mean the general drift of unsavoury characters coming up the Greenway - that was already happening by that point, wasn't it? Sort of a "He thinks they're bad, he should see what it would be like without us to pursue them constantly."
Or he could just be speaking poetically, the same way "forty days' march" doesn't necessarily mean exactly forty days, and is meant simply to imply a long time. Similarly, "within a day's march" could just mean "Closer than he wants, and capable of getting there quickly."
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Father, dear Father, if you see fit, We'll send my love to college for one year yet
Tie blue ribbons all about his head, To let the ladies know that he's married.
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