I wouldn't go so far as to say a schwa, but I'd do it with a little less emphasis and therefore a little less eh to the sound of the first there. As far as the grammar of the phrase there's (a(n), no) X, it is mirrored in several other Indo-European languages: German es gibt and the French il y a, as have been mentioned, and Spanish hay. The German, Spanish and French do not have distinct singular and plural forms as some fastidious grammarians would demand of the English. The English there's is, notwithstanding the grammarians' insistence otherwise, increasingly commonly seen in both singular and plural contexts.