"Rand Paul, using any available brick to throw at Obama"

In short a version of grandstanding. Schumer of NY uses any opportunity he can in the same way for certain issues.

While all politicians do this some are more likely than others to seize the moment.

In other words something is in the news and then all the sudden Senator "x" is writing a letter or demanding some action which gets him publicity.

It would be interesting to see how many times a press release is issued by these types that is not about some issue that has bubbled up first in the media. (My point being that I'd like to see if I am correct...or not.)

I do know that politicians are quick to write letters about anything and everything. But certain issues that have more PR potential seem to be more equal than others. My observation.

Why does Paul's motivation matter? I'm just happy to see something being done.

It does, because motivation decides what that "something" in "something being done" is.

Rand Paul's party is by far the biggest supporter of NSA, TSA, and other TLAs. If he really wanted to change things, he could start by convincing his own party to stop fellating the NSA.

I think injunctive relief against the NSA is a goal, a "something" that most civil liberties advocates and Rand Paul can agree on. Let it not be said that liberals took yet another opportunity to miss an opportunity at bipartisan reform of our executive branch's powers.

Motivation matters because you serve the goal, not the tactics. If Paul's motivation is not actually restricting the NSA, then at some point he's likely to pivot.

Where in Rand Paul's heavily libertarian-leaning history do you see evidence that he's in favor of a police state (or policies that make such possible), such that a massive issue like this is one on which he's likely to pivot away from his fundamental beliefs?

I know nothing of Rand Paul's history. When I see someone talking about an issue (the NSA) and using it to paint an opponent ("Obama's NSA"), then I think it's safe to say that the point is as much that opponent as the mere paint.