"We have to assume that they are going to continue to probe us and press us, and if they find that we are dropping our guard there will be negative consequences," he told CBS News producer Rob Hendin in an exclusive interview.
He argued that terrorist agencies are still "very active" across the globe. "Look at Somalia. We do see Westerners going to Somalia to fight, and if some of those go back home again, having been trained and battle hardened that's going to create a threat," he said noting that the U.S. efforts have "certainly put roadblocks in their ability to do that training."
Chertoff admitted he is concerned the U.S. defense against terrorism might lose political and public backing over time.
"I know that some of the threats we are facing, particularly in the medium to long term…So we are forced to asked the public and the politicians to be disciplined and committed to investing, even though the benefit of the investment may not be felt until five or ten years from now," he said.
Watch the interview above as well as CBS News' Bob Orr's analysis of the uproar over a Coast Guard training exercise this morning and a new Unplugged Under 40 segment on Kia Baskerville's day eight years ago.
"Washington Unplugged" appears live on CBSNews.com each weekday at 12:30 p.m. ET. Click here to check out previous episodes.