The South reacted to the election of Abraham Lincoln by eventually seceding from the Union. This, of course, prefigured the Civil War
During the Cold war, there was a big fear of a possible nuclear attack from the Soviet Union, so when the US wanted to increase its spending on defense, it argued for it by saying that it needed to have better weapons to be able to prevent a possible attack.
The correct answer to this open question is the following.
The power of Congress that Senator Paul probably most concerned about based on this passage is the Power to Declare War.
The United States Constitution states on Article I, section clause 1, that the United States Congress has the power to declare war. The Constitution grants Congress with expressed powers and this is one of them. That is why Senator Rand Paul is reflecting on the great responsibility Congress has regarding thus power of declaring war against another nation.