In addition to opposing Republican calls for a "touchback" provision, Napolitano also opposes asking border governors to certify the integrity of the border, a proposal pushed by Sen. John McCain, R-Ariz., during his presidential campaign.
"The certification issue sounds good," said Napolitano. "But it is a snapshot, not a sustained presence, and a snapshot could vary greatly within any given state within any given year."
Relying on governors to certify that the border is secure amounts to shirking responsibility, said Napolitano.
"If you make certification the only criteria for whether you then move into overall immigration reform, what I would be leery of is putting up a process by which you never have to take responsibility for overall immigration reform," she said.
ABC News' Arnab Datta and Ferdous Al-Faruque contributed to this report.