ABC's Mary McGuire reports:

Los Angeles Mayor Antonio Villaraigosa said fights on the debt ceiling and spending cuts should not distract Congress from efforts to fix a "broken immigration system" and introduce new comprehensive immigration legislation in 2013.

"They should be able to walk and chew gum at the same time," said Villaraigosa to a crowd of around 70 in Washington, D.C., Monday.

Villaraigosa characterized the current immigration system as "long on enforcement and short on opportunity."

The mayor also presented a six-part plan for achieving legal residency, which includes an employment verification system, border protection and criminal background checks.

"Legalization should be earned, but not be unattainable," said Villaraigosa, one of the top-elected Latino officials in the United States and a fierce advocate for a comprehensive immigratrion bill.

The mayor has also become active with other big-city mayors, such as New York Mayor Michael Bloomberg on the issue of gun violence. And one month after the shootings at Sandyhook Elementary School in Newtown, Conn., Villaraigosa repeated calls for tougher gun laws.

"It's an abomination that we don't have an assault weapons ban," said Villaraigosa.

Villagairosa also called for setting up universal background checks and a "beef up" of mental health resources.

As for his future in the public sector, Villaraigosa wouldn't give any specifics, saying only that he is "focusing on the job at hand" until the end of his mayoral term in June.

He is widely considered as a potential 2016 Democratic presidential candidate, or as a good contender to join President Obama's cabinet.

Villaraigosa previously served as the chairman of the 2012 Democratic National Convention.