Behind the drama there are deep currents, a tale of sex, drugs, violence and conservatism.
Senator Paul has, almost single-handedly, blocked the extension of the Patriot Act, seen by its opponents as the USA’s very own snooper’s charter.
It takes some guts to stand in the way of the US spy agencies, if only for a short while.
You might even think it an unconservative, rebellious, counter-cultural thing to do.
But, of course, US conservatism delights in tracing its roots to revolution.
Senator Paul ripped into the idea of the National Security Agency merely monitoring the flow of data, with an appeal to America’s origins.
“Our founders objected to the British soldiers writing warrants,” he said.
“They objected to them coming in their house and gathering their papers.
“Do you think our framers [of the constitution] would have been happy if the British government said, ‘OK, we’re just breaking your door down, we’re just getting your papers, but we’re not going to look at them?'”
This is of course grandstanding, by a leading contender to become the Republican presidential candidate, his behaviour a magnet for attention and probably money.
But he is tapping into a important, and often under-appreciated, strand of US politics: libertarianism.
It is not a strand of thought immediately obvious on the British political landscape, but I have a feeling it may be one of the forces and fault lines in Prime Minister David Cameron’s new government.
Rand Paul – at a glance
- an ophthalmologist and Kentucky senator
- a libertarian and Republican, also son of Ron Paul, who ran for president several times
- anti-surveillance and anti-drone, but conservative on same-sex marriage and abortion
- attacked by some in his party as being isolationist on foreign policy
- has testy relationship with senior party figures such as John McCain and Mitch McConnell
While the 2015 general election result may have been exciting, the campaign wasn’t.
Certainly, I saw none of the energy that was occasionally on display in the US 2012 presidential election.
Without doubt, the most intriguing, most unusual meetings I covered were rallies for Rand’s dad, Ron Paul, a habitual Republican contender.
Although Mr Paul Sr was then 77, in all my peregrinations around Europe, the US and the UK, I have never been to such youthful political gatherings.
Perhaps as importantly these were not geeky, tweedy and bow-tied students aping their elders. Instead, tattoos and piercings, shaved heads and mohicans abounded.
Blindfolded, spun round and plonked down in the hall, I might have thought I was waiting for a post-punk band, rather than an elderly politician.
Now you can overdo the importance of this. Ron Paul, after all, did not come close to winning his party’s nomination.
But these people were motivated by something that seemed new, or at least newly attractive.
What drew them wasn’t Ron Paul’s rather kooky thoughts about the gold standard, but his attitudes to war, and to the war on drugs.
There has been some questioning of how “real” a libertarian his son is, as Rand Paul trims his position in the pursuit of high office.
I think there are three touchstones: sex, drugs and violence.
It is hard to see how anyone who resents the power of the state could wish it to interfere in personal sexual orientation, and it isn’t much of an issue these days, although in the US some Christian conservatives may disagree.
Libertarians also don’t think it is the business of the government what poison you choose – while in the UK we are busy making legal highs illegal, they would make illegal highs legal.
This, too, is hardly outre these days, when marijuana has been decriminalised in four US states and Washington DC.
But fundamental to Ron and Rand’s view of a smaller state is one that does not throw its weight around on the world stage any more than it does at home.
Existing comfortably against this desire to cancel the last remnants of the “war on terror” is a militant opposition to state intrusion into people’s lives – exactly what the special senate session was all about.
These three tests are difficult for many on the right to pass – but they are also what make libertarianism such an interesting strand of thought.
There are plenty of faux libertarians around who fulminate about income tax and big government.
These three tests indicate whether they are merely against the state’s redistribution of wealth rather than in favour of a redistribution of power.
At first glance, you might think if there are any in the UK, then they are very shy indeed.
In fact, there is a Libertarian party, which did put up 15 candidates at the general election.
Could it be an appealing philosophy for a party looking for a new image?
The Liberal Democrats might be the most obvious adopters.
But they are still quivering in trauma, more concerned with working out how to function at all than what to do next.
Part of UKIP’s support may stem from a gut resentment against the statists’ impositions – their leaders could turn that into a more cerebral project but are unlikely to waste the energy this side of a European referendum.
Labour is certainly looking for some new ideas and hasn’t got much further than aspiration.
“Aspire”, while an excellent name for a forward-looking trade union, is a poor political philosophy.
Some within Labour are asking fundamental questions about the role of the state and where power should lie.
But for a party still scared of being seen “soft”, other issues of personal liberty may be harder to address.
But what intrigues me is whether libertarian trends will emerge in the Conservative Party – either as fault lines, or future philosophy.
The Conservative Party is already pretty liberal on matters of sexual choice.
Drugs are probably too touchy an area, with little or no political pressure to challenge the establishment consensus – as long as the real world can shelter behind the British virtue of hypocrisy.
Americans, in their naivety, like rules to reflect reality.
But war and its handmaidens of powerful security services have already caused queasiness on the backbenches in the last Parliament.
There is already a debate about the nature of this government.
There are those believers in a compassionate conservatism who look in the mirror and see the prime minister staring back, such as Steve Hilton, who believe David Cameron has a profound vision, a modern one-nation conservatism, replacing state with community but with the same aim as Disraeli – to eliminate the “two nations” of rich and poor.
But what may be key is the debate about the Human Rights Act.
Fundamental questions have been obscured by the peculiarly British conservative dislike of being told what to do by foreigners.
If stripped of this cover, 2015, the year we celebrate Magna Carta’s anniversary, may trigger a profound debate on the relationship between subjects and the state.
It improbable that Rand Paul will ever sit in the White House. Indeed, it is prettyunlikely he will win his party’s nomination.
But whether the views he reflects are embraced or scorned in Downing Street could be more than philosophically interesting, and have resonance in Syria, Strasbourg and, not least, Cheltenham – the home of GCHQ.