It seems to be somewhat particular about relation IDs. I have it working for Palo Alto, with relation ID 1544955. If you want to try this for your city, I recommend zooming in the city on openstreetmap.org, clicking the "Query features" button on the right side of the map (it's the cursor with a question mark icon), and clicking within the boundaries of you city. On the left side, a list of features will appear. Scroll down to enclosing features, and click on the appropriate entry. A relation name and number will be displayed at the top, with the OSM data below.
I hope this stays within the Overpass API server's usage limits. Processing Palo Alto caused the page to download ~85 MB from overpass-api.de, which asks users to stay below 10k queries and 5 GB per day. The OSM wiki lists other servers, some of which allow heavier usage.[0]