I assume you don't mean actually being elected Los Angeles City Attorney, right? You're talking about an assistant city attorney position?
eqprep's anecdotal evidence notwithstanding, you
will need good grades from a top school to work for the city attorney's office in L.A. (or in any other major city). You'll also need connections. Thus you'll want to try to land an internship there while you're a student, during the school year or summer.
Working for the city attorney's office is anything but a fall-back option. I suspect you'll find the positions are
harder to get than biglaw, not easier.
Positions with the city attorney in L.A., San Francisco, Portland, Seattle, etc. are in very high demand. In S.F., for instance, lawyers in the office come from Boalt, Stanford, Yale, Harvard, etc.--and I can't imagine the situation is too terribly different in L.A.
To get a sense of what I'm talking about, look at the résumé of the current L.A. City Atty, Rocky Delgadillo: Harvard undergrad, Columbia Law School, O’Melveny & Myers, etc.
http://www.lacity.org/atty/Meet_Rocky/attyrjdbo.htm
I think you'll find that the other attorneys in his office have similarly glittering résumés.