Closing the Door Completely
You're right. They did use the "of course" line once. As you noted that was the response Sen. Paul found unsatisfactory since it leaves the door open a crack. I suspect future answers to this same question will have to go farther. It would be quite a story if they refused to close the door on this completely after that day long filibuster calling attention to it.
BTW, I completely agree with you that Sen. Paul's message resonated outside the bubble. Ezra Klein, Josh Marshall, Greg Sargent and Piers Morgan all expressed some level of support for what he was doing. If people that far to the left were willing to cross party lines, I suspect most of the country is on Sen. Paul's side. This is a near unanimous political victory for Sen. Paul, which is another reason the White House won't dare to contradict him.
Update: Reason cites a poll which says 57% of Americans feel the targeting of citizens is unconstitutional. But the poll was completed before the filibuster. Seems likely that number would be higher now.