[1] Márquez was born in Los Angeles, California in 1968,[2] but her family later moved to Bisbee, Arizona in order to be closer to Sonora.

[3] From 2000 to 2014, Márquez worked in private law practice in Tucson, Arizona, focusing her efforts on federal criminal defense.

[3][4] During the 111th United States Congress, Democrats from the Arizona House delegation recommended Márquez to fill the vacancy on the United States District Court for the District of Arizona created by Judge Frank R. Zapata's decision to assume senior status.

[5] On June 23, 2011, during the 112th Congress, President Obama formally nominated Márquez to serve as a judge for the District of Arizona.

[6] Due to opposition by Arizona Senators John McCain and Jon Kyl, both Republicans, her nomination did not receive a hearing in the 112th Congress.