SCENARIOS: Major issues facing U.S. Homeland Security chief

(Reuters) - President-elect Barack Obama on Monday named Democratic Arizona Gov. Janet Napolitano as his Homeland Security secretary. Here are some of the top challenges she will face:

IMMIGRATION - Efforts to overhaul immigration laws stalled under President George W. Bush, leaving the fate of 12 million illegal immigrants uncertain and spurring public clamor for a more orderly system. Napolitano, at the forefront of the debate as governor of a state on the Mexican border, has called the current system "unenforced and unenforceable."

She has called for comprehensive reform including border security measures and a system to bring illegal immigrants "out of the economic shadows."

BORDER SECURITY - The new secretary will be responsible for completing a controversial barrier fence along parts of the U.S. border with Mexico, which has raised hackles with Mexico and local landowners. Plans for a high-tech "virtual fence" in other areas have been plagued by technical difficulties.

Napolitano drew wide attention in 2006 when she called out the National Guard to assist with border enforcement.

EMERGENCY MANAGEMENT - The botched federal response to Hurricane Katrina in 2005 tarnished the reputation of the Homeland Security Department and its component Federal Emergency Management Agency. The emergency agency was given higher marks in later disasters, but some experts say it should be removed from the department and stand on its own.

COUNTERTERRORISM - U.S. security officials warn of public complacency in vigilance against terrorism, and say al Qaeda still represents the most dangerous threat to U.S. safety.

FINANCIAL CRISIS - The financial crisis has put a severe crimp on the budgets of state and local security agencies, forcing some to divert federal homeland security aid for other purposes. Napolitano's experience as governor has been cited as useful in coping with the budget gaps.

(Reporting by Randall Mikkelsen in Washington; editing by David Storey)