He said that delivering the Prime Minister's Withdrawal Agreement - twice rejected by MPs by large majorities - would enable the Government to continue providing them with the support and resources they need.
Mr Wallace told BBC Radio 4's Today programme: "This morning I will meet the intelligence services and I will meet the police and all the people who protect us.
"They want us to get on with delivering a Brexit.
"They are professionals and they are looking after our safety, and if I were to look them in the eye and say:
"Should we just headlong fall into a collapse in Government or a collapse in Parliament? They would just despair."
"We are here to give them the support and resource they need as a Government, and voting for the deal is the way we will continue to be able to do that and how we will break from Europe."
In response, former Director of Communications for the Labour Party and prominent Remain supporter Alastair Campbell called Mr Wallace's comments "absolute nonsense".
"Security is weakened by this blind Brexit and it is a scandal he claims to speak for them all," he said.