Many resources will not allow searching by abbreviated journal title. Common abbreviated titles, such as JAMA for the Journal of the American Medical Association, have been added to Addison and Summon; most abbreviated titles required by citation style guides, such as J. Amer. Chem. Soc., are not searchable in Addison or databases. You will need to find the full title to look up these citations.
All That JAS is a source for looking up journal title abbreviations. Major sources listed there include the Gale Group Databases Title List, the ISI Master Journal List, and many discipline-specific journal title lists.
Books that list journal titles are available at the reference desks. Sources include Periodical title abbreviations, Acronyms, initialisms & abbreviations dictionary, and Chemical Abstracts Service source index. You can uses these books yourself or ask a librarian to lookup a short list of abbreviations for you.