You're going to hate this answer, but it's the true one: there is no bright-line guideline. US copyright law just doesn't work that way.
Section 108 of the Copyright Act grants libraries certain "superpowers" with respect to copying books for patrons when (and ONLY when) those works are not otherwise available for purchase at a reasonable cost. Additional Section 108 leeway is available with respect to journal articles. See the Section 108 Spinner for additional information.
Section 108 does not, however, cover individuals who copy library materials. While libraries are generally not required to police their photocopiers and scanners as long as they post boilerplate information about copyright near them, that doesn't mean that "I copied it in the library!" is a valid defense for a patron against infringement, because it isn't.
Such patrons, if accused of infringement, might have fair use as an affirmative defense; that would be a matter for the courts.