Here are some photos of Los Angeles voters doing their civic duty--the first taken on November 3, 1936, at the height of the Depression. (Roosevelt won a second term in that one.)
The second picture shows the same polling place (check the floor and the brickwork) on April 3, 1945. Those aren't newspapers the men are studying, but ballots. This was a municipal election, with low turnout--the line exists because only one voting booth was available.
Both these photos were copied from the LAPL's online Herald Examiner Photo Collection.
The building is the Los Angeles YMCA, which sat at 715-729 S. Hope Street for many years. Since the 1970s, though, the Sheraton Hotel Downtown has taken up the site, and then some.
Finally, here's a much older picture of the same lobby room, with the distinctive floor and brickwork.
The last picture is part of an online, annotated postcard collection held by CA State University Long Beach, called "A Visit to Old Los Angeles." This website, credited to Brent C. Dickerson, has a half-dozen views of the building, interior and exterior. You can see more pre-1920s postcards showing other buildings on Hope, such as the still-standing J.W. Robinson store (right across the street from the YMCA/Sheraton, at Grand).