All along, while casting a skeptical eye on the border fence going up, calling for the National Guard to patrol the border, advocating for a guest worker program to reduce illegal immigration, promising more local law enforcement cooperation with Mexico, Gov. Janet Napolitano of Arizona has repeated something like a mantra: Security and immigration are the federal government’s responsibility.

Now, it could be hers.

President-elect Barack Obama, transition officials said, is planning to choose Ms. Napolitano, a border-state governor who lives and breathes the often-heated immigration debate, to head the Homeland Security Department.