LOS ANGELES — Television’s highest-earning actress and a San Francisco art museum chief are two of the key figures in the bid to establish a new museum on the Mall devoted to the history and culture of American Latinos.

But Eva Longoria, who will rally public support for a bill in Congress to create the museum, and Jonathan Yorba, chairman of the museum-lobbying group that picked her, also played key roles in the creation of a problem-plagued Los Angeles museum and cultural center focused on the contributions of Mexican Americans in Southern California.

From 2004 to 2006, Yorba was the first executive director of La Plaza de Cultura y Artes, trying to lay the groundwork for the downtown L.A. museum that opened in April and almost immediately ran into financial difficulties....