It is well established in language acquisition research that monolingual children and adult second language learners misinterpret sentences with the universal quantifier "every" and make quantifier-spreading errors that are attributed to a preference for a match in number between two sets of objects. The present Visual World eye-tracking study tested bilingual heritage Russian-English adults and investigated how they interpret of sentences like "Every alligator lies in a bathtub" in both languages. Participants performed a sentence-picture verification task while their eye movements were recorded. Pictures showed three pairs of alligators in bathtubs and two extra objects: elephants (Control condition), bathtubs (Overexhaustive condition), or alligators (Underexhaustive condition). Monolingual adults performed at ceiling in all conditions. Heritage language (HL) adults made 20% q-spreading errors, but only in the Overexhaustive condition, and when they made an error they spent more time looking at the two extra bathtubs during the Verb region. We attribute q-spreading in HL speakers to cognitive overload caused by the necessity to integrate conflicting sources of information, i.e. the spoken sentences in their weaker, heritage, language and attention-demanding visual context, that differed with respect to referential salience.