The wide-ranging bill would pay for the hiring of 1,000 more border patrol agents, provide nearly $1 billion for countermeasures to biological weapons and eliminate a White House proposal to raise ticket fees for airline passengers by $3 to help finance other security programs.
Chertoff touched on other issues during the 50-minute interview the day after he announced broad changes at his 2-year-old department.
While he is still considering changes to the national color-coded threat advisory system, Chertoff praised its ability to target specific areas, as with the mass transit system that currently stands at code orange, or high alert, because of the London attacks.
He also said the economic and social attitude in the United States, compared to some European nations, "tends to reduce the amount of frustration" that can lead to terror attacks.
On a personal note, he recounted a moment a few years ago, before he took his current job, when he felt sheepish about reporting a suspicious package.
As it turned out, the package was not a threat, Chertoff said, But the instance highlighted in his mind how important it is for the public to keep a watchful eye - even if the hunch turns out to be wrong.
"I remember it crossed my mind, I said, 'Boy, am I overreacting?"' Chertoff said. "So I understand that personal dynamic. We have to repeatedly remind people not to be sheepish or embarrassed about taking those steps."